We propose a new deterministic robust design optimization method for composite laminate structures under worst-case material uncertainty. The method is based on a simultaneous parametrization of topology and material and combines a design problem and a material uncertainty problem into a single min–max optimization problem which provides an efficient approach to handle variation of material properties in stiffness driven design optimization problems. An analysis is performed using a design problem based on a failure criterion formulation to evaluate the ability of the proposed method to generate robust composite designs. The design problem is solved using various loads, boundary conditions and manufacturing constraints. The designs generated with the proposed method have improved objective responses compared to the worst-case response of designs generated with nominal material properties and are less sensitive to the variation of material properties. The analysis indicates that the proposed method can be efficiently applied in a robust structural optimization framework. © 2023 The Author(s)

We propose a method to analyze effects of material uncertainty in composite laminate structures optimized using a simultaneous topology and material optimization approach. The method is based on computing worst -case values for the material properties and provides an efficient way of handling variation in material properties of composites for stiffness driven optimization problems. An analysis is performed to evaluate the impact of material uncertainty on designs from two design problems: Maximization of stiffness and minimization of a failure criteria index, respectively. The design problems are solved using different loads, boundary conditions and manufacturing constraints. The analysis indicates that the influence of material uncertainty is dependent on the type of optimization problem. For compliance problems the impact on the objective value is proportional to the changes of the constitutive properties and the effect of material uncertainty is consistent and predictable for the generated designs. The strength-based problem shows that material uncertainty has a significant impact on the response, and the effects of material uncertainty is not consistent and changes for different design requirements. In addition, the results show an increase of up to 25% of the maximum failure index when considering the worst-case deviation of the constitutive properties from their nominal values.

We propose a topology optimization-based method for optimal design of cooling systems in the form of a mathematical game between two players trying to reach a compromise between limiting the amount of a cooling medium used and obtaining low temperatures in the design domain. The flow of the cooling medium is governed by a Stokes-Brinkman flow model with penalty, while the temperature is governed by a stationary convection-diffusion problem whose solution is approximated using a finite element method with consistent stabilization. Existence of solution for the continuum problems and finite element convergence are shown. The idea and performance of the proposed design method are illustrated by numerical examples based on a problem-setting inspired by an industrial design problem for a gas turbine part. The method exhibits good convergence and is able to generate meaningful design concepts representing various levels of compromise between limited use of cooling medium and low temperatures.

We present a worst-case approach to topology optimization (TO) for maximum stiffness under boundary displacement parametrized by a matrix-valued scaling function times an uncertain vector giving its direction. The objective function in the TO problem is the minimum of the potential energy maximized over the set of boundary displacements, which in the absence of prescribed loads means maximizing the reaction loads arising from enforcing the boundary displacement. It is shown that the TO problem can be cast as the minimization of the maximum eigenvalue of a matrix depending on solutions to a small number of (linear elastic) state problems. Numerical solution of this potentially non-smooth problem using algorithms for smooth optimization, a non-linear semi-definite programming reformulation, and a non-smooth bundle method is discussed and tested. CO 2021 The Author. Published by Elsevier Ltd. This is an open access article under the CC BY license (http:// creativecommons.org/licenses/by/4.0/).

An efficiency-enhanced procedure to treat continuous-time, high-cycle fatigue (HCF) constraints in topology optimization is presented. The HCF model predicts the evolution of fatigue damage at each point in the design domain using a system of ordinary differential equations. We employ gradient-based optimization and the fatigue sensitivities are determined using adjoint sensitivity analysis. As the predicted damage has history dependence, adjoint variables are solved via a stepwise backward procedure. Therefore, the computational cost increases in proportion to the number of time steps. To reduce this cost, we propose an extrapolation technique which is valid for all forms of periodic, proportional loads and most non-proportional loads and allows treatment of essentially an unlimited number of load cycles. Using this technique, several problems in both 2D and 3D are solved numerically where the objective is to minimize structural mass subjected to a fatigue constraint.

In this study, we consider identification of parameters in a non-linear continuum-mechanical model of arteries by fitting the models response to clinical data. The fitting of the model is formulated as a constrained non-linear, non-convex least-squares minimization problem. The model parameters are directly related to the underlying physiology of arteries, and correctly identified they can be of great clinical value. The non-convexity of the minimization problem implies that incorrect parameter values, corresponding to local minima or stationary points may be found, however. Therefore, we investigate the feasibility of using a branch-and-bound algorithm to identify the parameters to global optimality. The algorithm is tested on three clinical data sets, in each case using four increasingly larger regions around a candidate global solution in the parameter space. In all cases, the candidate global solution is found already in the initialization phase when solving the original non-convex minimization problem from multiple starting points, and the remaining time is spent on increasing the lower bound on the optimal value. Although the branch-and-bound algorithm is parallelized, the overall procedure is in general very time-consuming.

We present a new topology optimization problem formulation for conjugate heat transfer problems based on minimizing temperature subject to mass flow constraints on the flow of a cooling medium and show well-posedness of the continuum problem. A version of the problem augmented with a lower bound on the stiffness of the designs is considered in numerical examples loosely based on a real design case for a gas turbine part. The numerical examples indicate that the proposed problem formulation can be used to obtain designs which are useful from an engineering perspective.

A topology optimization formulation including a model of the layer-by-layer additive manufacturing (AM) process is considered. Defined as a multi-objective minimization problem, the formulation accounts for the performance and cost of both the final and partially manufactured designs and allows for considering AM-related issues such as overhang and residual stresses in the optimization. The formulation is exemplified by stiffness optimization in which the overhang is limited by adding mechanical or thermal compliance as a measure of the cost of partially manufactured designs. Convergence of the model as the approximate layer-by-layer model is refined is shown theoretically, and an extensive numerical study indicates that this convergence can be fast, thus making it a computationally viable approach useful for including AM-related issues into topology optimization. The examples also show that drips and sharp corners associated with some geometry-based formulations for overhang limitation can be avoided. The codes used in this article are written in Python using only open sources libraries and are available for reference.

This paper presents a new discrete parametrization method for simultaneous topology and material optimization of composite laminate structures, referred to as Hyperbolic Function Parametrization (HFP). The novelty of HFP is the way the candidate materials are parametrized in the optimization problem. In HFP, a filtering technique based on hyperbolic functions is used, such that only one design variable is used for any given number of material candidates. Compared to state-of-the-art methods such Discrete Material and Topology Optimization (DMTO) and Shape Function with Penalization (SFP), HFP has much fewer optimization variables and constraints but introduces additional non-linearity in the optimization problems. A comparative analysis of HFP, DMTO and SFP are performed based on the problem of maximizing the stiffness of composite plates under a total volume constraint and multiple manufacturing constraints using various loads, boundary conditions and input parameters. The comparison shows that all three methods are highly sensitive to the choice of input parameters for the optimization problem, although the performance of HFP is overall more consistent. HFP method performs similarly to DMTO and SFP in terms of the designs obtained and computational cost. However, HFP obtains similar or better objective function values compared to the DMTO and SFP methods.

In this paper an existing in vivo parameter identification method for arteries is extended to account for smooth muscle activity. Within this method a continuum-mechanical model, whose parameters relate to the mechanical properties of the artery, is fit to clinical data by solving a minimization problem. Including smooth muscle activity in the model increases the number of parameters. This may lead to overparameterization, implying that several parameter combinations solve the minimization problem equally well and it is therefore not possible to determine which set of parameters represents the mechanical properties of the artery best. To prevent overparameterization the model is fit to clinical data measured at different levels of smooth muscle activity. Three conditions are considered for the human abdominal aorta: basal during rest; constricted, induced by lower-body negative pressure; and dilated, induced by physical exercise. By fitting the model to these three arterial conditions simultaneously a unique set of model parameters is identified and the model prediction agrees well with the clinical data.

Designs obtained with topology optimization (TO) are usually not safe against damage. In this paper, density-based TO is combined with a moving morphable component (MMC) representation of structural damage in an optimization problem for fail-safe designs. Damage is inflicted on the structure by an MMC which removes material, and the goal of the design problem is to minimize the compliance for the worst possible damage. The worst damage is sought by optimizing the position of the MMC to maximize the compliance for a given design. This non-convex problem is treated using a gradient-based solver by initializing the MMC at multiple locations and taking the maximum of the compliances obtained. The use of MMCs to model damage gives a finite element-mesh-independent method, and by allowing the components to move rather than remain at fixed locations, more robust structures are obtained. Numerical examples show that the proposed method can produce fail-safe designs with reasonable computational cost.

We propose a topology optimization method for design of transversely isotropic elastic continua subject to high-cycle fatigue. The method is applicable to design of additive manufactured components, where transverse isotropy is often manifested in the form of a lower Youngs modulus but a higher fatigue strength in the build direction. The fatigue constraint is based on a continuous-time model in the form of ordinary differential equations governing the time evolution of fatigue damage at each point in the design domain. Such evolution occurs when the stress state lies outside a so-called endurance surface that moves in stress space depending on the current stress and a back-stress tensor. Pointwise bounds on the fatigue damage are approximated using a smooth aggregation function, and the fatigue sensitivities are determined by the adjoint method. Several problems where the objective is to minimize mass are solved numerically. The problems involve non-periodic proportional and non-proportional load histories. Two alloy steels, AISI-SAE 4340 and 34CrMo6, are treated and the respective as well as the combined impact of transversely isotropic elastic and fatigue properties on the design are compared.

We consider topology optimization of Stokes flow with traction boundary conditions using finite elements with low-order velocity-approximation and an element-wise constant hydrostatic pressure. The finite element formulation is stabilized using a penalty on the jump in pressure between adjacent elements. Convergence of solutions to the finite element-discretized topology optimization problem is shown, and several optimization problems are solved using a preconditioned conjugate gradient solver for the finite element matrix problem. Stable convergence to high-quality designs without an excessive number of linear solver iterations is observed, and it is seen that the finite element formulation is not particularly sensitive to the choice of the pressure jump penalty parameter, thus making it a practically useful method. (C) 2021 The Author(s). Published by Elsevier B.V.

The properties of the continuous-time, high-cycle fatigue model of Ottosen et al. (2008) is investigated for challenging stress states. We derive an analytical solution to the damage per cycle for cyclic, proportional stress. Numerical investigations for 7050-T7451 aluminum alloy and AISI 4340 steel alloy show exponential convergence to a constant damage per cycle for cyclic proportional stress, and Wynns epsilon algorithm for sequence acceleration improves the convergence rate. Fatigue damage is well predicted for an applied proportional stress, but damage is severely underpredicted for rotary stress states or combinations of tension/compression and torsion.

We consider structural optimization (SO) under uncertainty formulated as a mathematical game between two players -- a "designer" and "nature". The first player wants to design a structure that performs optimally, whereas the second player tries to find the worst possible conditions to impose on the structure. Several solution concepts exist for such games, including Stackelberg and Nash equilibria and Pareto optima. Pareto optimality is shown not to be a useful solution concept. Stackelberg and Nash games are, however, both of potential interest, but these concepts are hardly ever discussed in the literature on SO under uncertainty. Based on concrete examples of topology optimization of trusses and finite element-discretized continua under worst-case load uncertainty, we therefore analyze and compare the two solution concepts. In all examples, Stackelberg equilibria exist and can be found numerically, but for some cases we demonstrate nonexistence of Nash equilibria. This motivates a view of the Stackelberg solution concept as the correct one. However, we also demonstrate that existing Nash equilibria can be found using a simple so-called decomposition algorithm, which could be of interest for other instances of SO under uncertainty, where it is difficult to find a numerically efficient Stackelberg formulation.

Metal AM (additive manufacturing) components are generally inhomogeneous and have different microstructure in the bulk compared with (contour) regions near the surface. This, as well as rough as-built surfaces, affects mechanical properties. In this paper, we develop a topology optimization method that considers such inhomogeneities. The method is a direct extension of standard density-based methods using linear filtering for regularization, and a second filtering of the design variables is used to identify a surface layer, the thickness of which is given by the filter radius. Domain extension is used in order to properly identify such layers at the boundary of the design domain. The method is generally applicable but is demonstrated for stiffness optimization. Both two- and three-dimensional problems are treated. A general property of the method is that the topological complexity is reduced, i.e. the optimized designs get fewer and thicker structural members as the width of the surface layer is increased.

In many applications, it is of interest to perform static finite element analyses on freely floating bodies that are not in quasi-static equilibrium; airplanes and helicopters maneuvering in flight for example. This is particularly so if topology optimization (TO) is to be used, since TO with dynamic analyses can be very computationally expensive. The so-called inertia relief method, which essentially entails computing the rigid body inertia and subtracting it from the given loads to make the system of loads self-equilibrating, can sometimes be used to replace a dynamic analysis with a static, thus enabling the use of high-resolution TO. We derive the inertia relief method for elastic continua and obtain a static variational problem which require that we can suppress (linearized) rigid body motions without affecting the deformation. Three methods for doing this are investigated. Based on the static variational problem we consider maximizing stiffness using TO. Numerical examples show that all three methods for suppressing rigid body motion work, and indicate that optimal designs for freely floating structures undergoing rigid acceleration can differ significantly from designs optimized under static conditions. (C) 2019 Elsevier B.Y. All rights reserved.

We propose a topology optimization method that includes high-cycle fatigue as a constraint. The fatigue model is based on a continuous-time approach where the evolution of damage in each point of the design domain is governed by a system of ordinary differential equations, which employs the concept of a moving endurance surface being a function of the stress and back stress. Development of fatigue damage only occurs when the stress state lies outside the endurance surface. The fatigue damage is integrated for a general loading history that may include non-proportional loading. Thus, the model avoids the use of a cycle-counting algorithm. For the global high-cycle fatigue constraint, an aggregation function is implemented, which approximates the maximum damage. We employ gradient-based optimization, and the fatigue sensitivities are determined using adjoint sensitivity analysis. With the continuous-time fatigue model, the damage is load history dependent and thus the adjoint variables are obtained by solving a terminal value problem. The capabilities of the presented approach are tested on several numerical examples with both proportional and non-proportional loads. The optimization problems are to minimize mass subject to a high-cycle fatigue constraint and to maximize the structural stiffness subject to a high-cycle fatigue constraint and a limited mass.

A method for identifying mechanical properties of arterial tissue in vivo is proposed in this paper and it is numerically validated for the human abdominal aorta. Supplied with pressure-radius data, the method determines six parameters representing relevant mechanical properties of an artery. In order to validate the method, 22 finite element arteries are created using published data for the human abdominal aorta. With these in silico abdominal aortas, which serve as mock experiments with exactly known material properties and boundary conditions, pressure-radius data sets are generated and the mechanical properties are identified using the proposed parameter identification method. By comparing the identified and pre-defined parameters, the method is quantitatively validated. For healthy abdominal aortas, the parameters show good agreement for the material constant associated with elastin and the radius of the stress-free state over a large range of values. Slightly larger discrepancies occur for the material constants associated with collagen, and the largest relative difference is obtained for the in situ axial prestretch. For pathological abdominal aortas incorrect parameters are identified, but the identification method reveals the presence of diseased aortas. The numerical validation indicates that the proposed parameter identification method is able to identify adequate parameters for healthy abdominal aortas and reveals pathological aortas from in vivo-like data.

Several filter approaches that introduce additive manufacturing-related overhang constraints in topology optimization exist. However, a drawback of these is that exact satisfaction of overhang constraints produces sharp inward corners resulting in stress singularities. The present paper therefore modifies such filter approaches by a penalty formulation, where the choice of penalty factor regulates how closely the overhang constraint is satisfied. By appropriately choosing certain weight factors in the penalty function, the cost of support structures is also reflected in the formulation in a simple and computationally inexpensive way. The method is demonstrated by parameter studies using the classical MBB beam, using both structured and unstructured meshes.

We consider a model for density-based topology optimization (TO) of stationary heat transfer problems with design-dependent internal convection in 3D structures with periodic design obtained by extruding a 2D design in 3D. The internal convection takes place at the interface between a solid material and a cooling fluid in internal channels through the design domain. The objective of the TO is to minimize the maximum temperature, which is approximated by means of an L-p norm. The finite element method is used to discretize the state problem and the resulting optimization problem is solved using gradient-based methods. The internal convection is modeled to be dependent on the design density gradient in the continuous problem. In discrete form, it is approximated as proportional to the difference in design densities of adjacent elements in the finite element mesh. The theory is illustrated by numerical examples based on a simplified guide vane geometry.

We develop a topology optimization method including high-cycle fatigue as a constraint. The fatigue model is based on a continuous-time approach, which uses the concept of a moving endurance surface as a function of the stress history and back stress evolution. The development of damage only occurs when the stress state lies outside the endurance surface. Furthermore, an aggregation function, which approximates the maximum fatigue damage, is implemented. As the optimization workflow is sensitivity-based, the fatigue sensitivities are determined using an adjoint sensitivity analysis. The capabilities of the presented approach are tested on numerical models where the problem is to maximize the stiffness subject to high-cycle fatigue constraints.

We present a worst-case approach for topology optimization under load-uncertainty based on a general problem formulation involving maxima of quadratic functions of an uncertain load vector as both objective and constraints. The problem is reformulated as a non-linear semi-definite program which can be solved efficiently. An important special case of the general problem formulation is worst-case compliance minimization under worst-case stress constraints which is illustrated by numerical examples. (C) 2017 Elsevier B.V. All rights reserved.

The paper concerns robustness with respect to uncertain loading in topology optimization problems with essentially arbitrary objective functions and constraints. Using a game theoretic framework we formulate problems, or games, defining Nash equilibria. In each game a set of topology design variables aim to find an optimal topology, while a set of load variables aim to find the worst possible load. Several numerical examples with uncertain loading are solved in 2D and 3D. The games are formulated using global stress, mass and compliance as objective functions or constraints.

Many problems in structural optimization can be formulated as a minimization of the maximum eigenvalue of a symmetric matrix. In practise it is often observed that the maximum eigenvalue has multiplicity greater than one close to or at optimal solutions. In this note we give a sufficient condition for this to happen at extreme points in the optimal solution set. If, as in topology optimization, each design variable determines the amount of material in a finite element in the design domain then this condition essentially amounts to saying that the number of elements containing material at a solution must be greater than the order of the matrix.

Contractions of uterine smooth muscle cells consist of a chain of physiological processes. These contractions provide the required force to expel the fetus from the uterus. The inclusion of these physiological processes is, therefore, imperative when studying uterine contractions. In this study, an electro-chemo-mechanical model to replicate the excitation, activation, and contraction of uterine smooth muscle cells is developed. The presented modeling strategy enables efficient integration of knowledge about physiological processes at the cellular level to the organ level. The model is implemented in a three-dimensional finite element setting to simulate uterus contraction during labor in response to electrical discharges generated by pacemaker cells and propagated within the myometrium via gap junctions. Important clinical factors, such as uterine electrical activity and intrauterine pressure, are predicted using this simulation. The predictions are in agreement with clinically measured data reported in the literature. A parameter study is also carried out to investigate the impact of physiologically related parameters on the uterine contractility.

Problem solving is at the heart of the mechanics curriculum, and developing problem solving skills is an important learning objective in basic and advanced mechanics courses at the undergraduate level. In alignment with this tradition, written examinations are mainly designed to test problem solving capabilities. Despite the fact that students spend most of their mechanics studies solving mechanics problems, an alarming fraction of them fail the written examination. One possible explanation is that a problem solving infrastructure, e.g. answers to problems and opportunities for collaboration with fellow students, is provided during the study period of courses, but missing during the examination.

Structures designed by topology optimization (TO) are frequently sensitive to loads different from the ones accounted for in the optimization. In extreme cases this means that loads differing ever so slightly from the ones it was designed to carry may cause a structure to collapse. It is therefore clear that handling uncertainty regarding the actual loadings is important. To address this issue in a systematic  manner is one of the main goals in the field of robust TO. In this work we present a deterministic robust formulation of TO for maximum stiffness design which accounts for uncertain variations around a set of nominal loads. The idea is to find a design which minimizes the maximum compliance obtained as the loads vary in infinite, so-called uncertainty sets. This naturally gives rise to a semi-infinite optimization problem, which we here reformulate into a non-linear, semi-definite program. With appropriate numerical algorithms this optimization problem can be solved at a cost similar to that of solving a standard multiple load-case TO problem with the number of loads equal to the number of spatial dimensions plus one, times the number of nominal loads. In contrast to most previously suggested methods, which can only be applied to small-scale problems, the presented method is – as illustrated by a numerical example – well-suited for large-scale TO problems.

This paper concerns optimal design of so-called Neuro-Mechanical Oscillators (NMOs). An NMO is a new type of bio-inspired mechatronic system which consists of an actuated truss with a recurrent neural network (RNN) superimposed onto it. By choosing the entries of the weight matrix of the RNN, an NMO can be designed, using numerical optimization, to generate pre-specified time-varying motions when subject to certain time-varying input signals. However, to rule out possible dependence of the motion on the initial state of the system as well as convergence into limit cycles, some form of constraints must be imposed on the system's design parameters. To derive such constraints, we investigate under what conditions the influence of the initial state eventually vanishes and the motion becomes completely determined by the input signal. Three sufficient criteria are presented for RNNs, but the possibility of large mechanical deformations most likely rule out global system level results. For sufficiently small deformations, however, local results are obtained, and a numerical example provided in the paper indicates that these can be useful for designing practical systems.

The paper concerns worst-case compliance optimization by finding the structural topology with minimum compliance for the loading due to the worst possible acceleration of the structure and attached non-structural masses. A main novelty of the paper is that it is shown how this min-max problem can be formulated as a non-linear semi-definite programming (SDP) problem involving a small-size constraint matrix and how this problem is solved numerically. Our SDP formulation is an extension of an eigenvalue problem seen previously in the literature; however, multiple eigenvalues naturally arise which makes the eigenvalue problem non-smooth, whereas the SDP problem presented in this paper provides a computationally tractable problem. Optimized designs, where the uncertain loading is due to acceleration of applied masses and the weight of the structure itself, are shown in two and three dimensions and we show that these designs satisfy optimality conditions that are also presented.

Training of recurrent neural networks is typically formulated as unconstrained optimization problems. There is, however, an implicit constraint stating that the equations of state must be satisfied at every iteration in the optimization process. Such constraints can make a problem highly non-linear and thus difficult to solve. A potential remedy is to reformulate the problem into one in which the parameters and state are treated as independent variables and all constraints appear explicitly. In this paper we compare an implicitly and an explicitly constrained formulation of the same problem. Reported numerical results suggest that the latter is in some respects superior.

This paper concerns an issue that may arise in design optimization of dynamical systems that possess multiple equilibrium points. If one considers only such points, it is possible to pose optimization problems in which the state problem is treated as a static problem. This is attractive as it reduces the computational cost compared to approaches which account for the entire state trajectory. However, if the system has multiple equilibria, it could happen that the equilibrium point attained when the system was optimized has only a small region of attraction. This means that in order to attain the desired state, the system must be initialized in its close vicinity, something which may be difficult in practise. In the paper we demonstrate this issue by considering design optimization of Neuro-Mechanical Shape Memory Devices (NMSMDs), a type of mechatronic systems that take on prescribed shapes when subjected to certain input stimuli introduced by the authors in an earlier paper. The conclusion is that although the static problem formulation considered has some attractive features, the existence of multiple equilibria for the governing equations of NMSMDs seems to necessitate the use of dynamic problem formulations.

This paper concerns optimization of active mechanical systems capable of exhibiting persistent oscillatory behavior. In part inspired by biological systems possessing similar properties we refer to these systems as neuro-mechanical oscillators. The mathematical model consists of a set of nonlinear ordinary differential equations describing an actuated truss excited by a nonlinear recurrent neural network. An optimization problem is formulated with the goal of adjusting some of the parameters in the system such that when the neural network is subjected to a constant input, one of the nodes in the truss follows a prescribed trajectory in a periodic fashion. Two examples are presented to illustrate the concept, and the corresponding optimization problems are solved numerically.

In this paper we describe the modeling and optimization of what we refer to as Neuro-Mechanical Shape Memory Devices (NMSMDs). These are active mechanical structures which are designed to take on specific shapes in response to certain external stimuli. An NMSMD is a particular example of a Neuro-Mechanical Network (NMN), a mechanical structure that consists of a network of simple but multifunctional elements. In the present work, each element contains an actuator and an artificial neuron, and when assembled into a structure the elements form an actuated truss with a superimposed recurrent neural network.

The task of designing an NMSMD is cast as an optimization problem in which a measure of the error between the actual and desired shape for a number of given stimuli is minimized. The optimization problems are solved using a gradient based solver, and some numerical examples are provided to illustrate the results from the design process and some aspects of the proposed model.

Many biological and artificial systems are made up from similar, relatively simple elements that interact directly with their nearest neighbors. Despite the simplicity of the individual building blocks, systems of this type, network systems, often display complex behavior — an observation which has inspired disciplines such as artificial neural networks and modular robotics. Network systems have several attractive properties, including distributed functionality, which enables robustness, and the possibility to use the same elements in different configurations. The uniformity of the elements should also facilitate development of efficient methods for system design, or even self-reconfiguration. These properties make it interesting to investigate the idea of constructing mechatronic systems based on networks of simple elements.

This thesis concerns modeling and optimal design of a class of active mechanical network systems referred to as Neuro-Mechanical Networks (NMNs). To make matters concrete, a mathematical model that describes an actuated truss with an artificial recurrent neural network superimposed onto it is developed and used. A typical NMN is likely to consist of a substantial number of elements, making design of NMNs for various tasks a complex undertaking. For this reason, the use of numerical optimization methods in the design process is advocated. Application of such methods is exemplified in four appended papers that describe optimal design of NMNs which should take on static configurations or follow time-varying trajectories given certain input stimuli. The considered optimization problems are nonlinear, non-convex, and potentially large-scale, but numerical results indicate that useful designs can be obtained in practice.

The last paper in the thesis deals with a solution method for optimization problems with matrix inequality constraints. The method described was developed primarily for solving optimization problems stated in some of the other appended papers, but is also applicable to other problems in control theory and structural optimization.

This thesis concerns modeling and optimal design of Neuro-Mechanical Networks. A Neuro-Mechanical Network (NMN) can be described as an active mechanical structure, made up from a network of simple but multifunctional elements that interact with their nearest neighbors. The concept is of mechatronic character as it involves integration of actuators, sensors, signal processing, and control, into a mechanical structure.

The first part of the thesis consists of three chapters. The first of these chapters contains a brief introduction to the NMN-concept and the present work. In the second chapter, the particular type of NMNs considered here is described in more detail, and the third chapter constitute a brief survey of some works relevant to optimization of active structures, including enabling technologies and static and dynamic shape control.

The second part of the thesis consists of two papers, where the first paper describes optimal design of NMNs for static shape control, while the second paper is concerned with optimal design of structures that exhibit oscillatory motion.

A method for estimation of central arterial pressure based on linear one-dimensional wave propagation theory is presented in this paper. The equations are applied to a distributed model of the arterial tree, truncated by three-element windkessels. To reflect individual differences in the properties of the arterial trees, we pose a minimization problem from which individual parameters are identified. The idea is to take a measured waveform in a peripheral artery and use it as input to the model. The model subsequently predicts the corresponding waveform in another peripheral artery in which a measurement has also been made, and the arterial tree model is then calibrated in such a way that the computed waveform matches its measured counterpart. For the purpose of validation, invasively recorded abdominal aortic, brachial, and femoral pressures in nine healthy subjects are used. The results show that the proposed method estimates the abdominal aortic pressure wave with good accuracy. The root mean square error (RMSE) of the estimated waveforms was 1.61 ± 0.73 mmHg, whereas the errors in systolic and pulse pressure were 2.32 ± 1.74 and 3.73 ± 2.04 mmHg, respectively. These results are compared with another recently proposed method based on a signal processing technique, and it is shown that our method yields a significantly (P < 0.01) lower RMSE. With more extensive validation, the method may eventually be used in clinical practice to provide detailed, almost individual, specific information as a valuable basis for decision making. Copyright © 2008 the American Physiological Society.

This paper is about a simple method for solving nonlinear, non-convex optimization problems (NLPs) with matrix inequality constraints. The method is based on the fact that a symmetric matrix is positive semi-definite if and only if it admits a Cholesky decomposition, and works by reformulating the original matrix inequality constrained problem into a standard NLP, for which there are currently many high-quality codes available. Examples of optimization problems involving matrix inequality constraints are relatively frequent in the structural optimization literature, and to illustrate a potential usage of our method we present numerical solutions for weight minimization of trusses subject to compliance and global buckling constraints. Looking ahead, we also see problems involving simultaneous optimization of both structure and control systems being common, and since matrix inequality constrained problems appear frequently in control theory, we believe that the number of applications for codes like the one presented here will continue to grow rapidly.

Neuro-Mechanical Shape Memory Devices (NMSMDs) are a new type of active mechanical systems designed to take on prescribed shapes when subjected to a certain input stimuli. In an earlier paper we derived a mathematical model for NMSMDs and posed an optimization problem for finding system parameters that would result in an NMSMD with a certain desired behavior. The optimization problem was highly nonlinear and non-convex, making it difficult to find good solutions. In this paper, through using a numerical example, we show that these difficulties can be alleviated by a new formulation of the original optimization problem. However, it is also shown that, due to the possible existence of multiple equilibrium points for the governing equations of NMSMDs, solutions to the new optimization problem must be carefully validated.