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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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Phenomena such as biological growth and damage evolution can be thought of as time evolving processes, the directions of which are governed by descendent of certain goal functions. Mathematically this means using a dynamical systems approach to optimization. We extend such an approach by introducing a field quantity, representing nutrients or other non-mechanical stimuli, that modulate growth and damage evolution. The derivation of a generic model is systematic, starting from a Lyaponov-type descent condition and utilizing a Coleman-Noll strategy. A numerical algorithm for finding stationary points of the resulting dynamical system is suggested and applied to two model problems where the influence of different levels of nutrient sensitivity are observed. The paper demonstrates the use of a new modeling technique and shows its application in deriving a generic problem of growth and damage evolution. [ABSTRACT FROM AUTHOR]

We present a contribution to a relatively unexplored application of topology optimization: structural topology optimization with fatigue constraints. A probability based high-cycle fatigue analysis is combined with principal stress calculations in order to find the topology with minimum mass that can withstand prescribed variable-amplitude loading conditions for a specific life time. This allows us to generate optimal conceptual designs of structural components where fatigue life is the dimensioning factor. We describe the fatigue analysis and present ideas that make it possible to separate the fatigue analysis from the topology optimization. The number of constraints is kept low as they are applied to stress clusters, which are created such that they give adequate representations of the local stresses. Optimized designs constrained by fatigue and static stresses are shown and a comparison is also made between stress constraints based on the von Mises criterion and the highest tensile principal stresses. The paper is written with focus on structural parts in the avionic industry, but the method applies to any load carrying structure, made of linear elastic isotropic material, subjected to repeated loading conditions. [ABSTRACT FROM AUTHOR]

This paper develops and evaluates a method for handling stress constraints in topology optimization. The stress constraints are used together with an objective function that minimizes mass or maximizes stiffness, and in addition, the traditional stiffness based formulation is discussed for comparison. We use a clustering technique, where stresses for several stress evaluation points are clustered into groups using a modified P-norm to decrease the number of stress constraints and thus the computational cost. We give a detailed description of the formulations and the sensitivity analysis. This is done in a general manner, so that different element types and 2D as well as 3D structures can be treated. However, we restrict the numerical examples to 2D structures with bilinear quadrilateral elements. The three formulations and different approaches to stress constraints are compared using two well known test examples in topology optimization: the L-shaped beam and the MBB-beam. In contrast to some other papers on stress constrained topology optimization, we find that our formulation gives topologies that are significantly different from traditionally optimized designs, in that it actually manage to avoid stress concentrations. It can therefore be used to generate conceptual designs for industrial applications. [ABSTRACT FROM AUTHOR]

The dynamical systems approach to sizing and SIMP topology optimization, introduced in a previous paper, is extended to the case of time-varying loads. A general dynamical system, satisfying a Lyaponov-type descent condition, is derived and specialized to a goal function combining stiffness and mass. For a cyclic time-dependent load it is indicated how, in the limit of short cycles compared to the overall time scale, this can be handled by multiple load cases. Numerical examples, both for a convex and a non-convex case, illustrates the theory. [ABSTRACT FROM AUTHOR]

This paper uses a dynamical systems approach for studying the material distribution (density or SIMP) formulation of topology optimization of structures. Such an approach means that an ordinary differential equation, such that the objective function is decreasing along a solution trajectory of this equation, is constructed. For stiffness optimization two differential equations with this property are considered. By simple explicit Euler approximations of these equations, together with projection techniques to satisfy box constraints, we obtain different iteration formulas. One of these formulas turns out to be the classical optimality criteria algorithm, which, thus, is receiving a new interpretation and framework. Based on this finding we suggest extensions of the optimality criteria algorithm. A second important feature of the dynamical systems approach, besides the purely algorithmic one, is that it points at a connection between optimization problems and natural evolution problems such as bone remodeling and damage evolution. This connection has been hinted at previously but, in the opinion of the authors, not been clearly stated since the dynamical systems concept was missing. To give an explicit example of an evolution problem that is in this way connected to an optimization problem, we study a model of bone remodeling. Numerical examples, related to both the algorithmic issue and the issue of natural evolution represented as bone remodeling, are presented. [ABSTRACT FROM AUTHOR]

The field of topology optimization is well developed for load carrying trusses, but so far not for other similar network problems. The present paper is a first study in the direction of topology optimization of flow networks. A linear network flow model based on Hagen–Poiseuille’s equation is used. Cross-section areas of pipes are design variables and the objective of the optimization is to minimize a measure, which in special cases represents dissipation or pressure drop, subject to a constraint on the available (generalized) volume. A ground structure approach where cross-section areas may approach zero is used, whereby the optimal topology (and size) of the network is found.A substantial set of examples is presented: small examples are used to illustrate difficulties related to non-convexity of the optimization problem; larger arterial tree-type networks, with bio-mechanics interpretations, illustrate basic properties of optimal networks; the effect of volume forces is exemplified.We derive optimality conditions which turns out to contain Murray’s law; thereby, presenting a new derivation of this well known physiological law. Both our numerical algorithm and the derivation of optimality conditions are based on an ϵ-perturbation where cross-section areas may become small but stay finite. An indication of the correctness of this approach is given by a theorem, the proof of which is presented in an appendix. [Copyright &y& Elsevier]