Phase-field approaches to structural topology optimization

The mean compliance minimization in structural topology optimization is solved with the help of a phase field approach. Two steepest descent approaches based on L2- and H-1 gradient flow dynamics are discussed. The resulting flows are given by Allen-Cahn and Cahn-Hilliard type dynamics coupled to a linear elasticity system. We finally compare numerical results obtained from the two different approaches

Relating phase field and sharp interface approaches to structural topology optimization

A phase field approach for structural topology optimization which allows for topology changes and multiple materials is analyzed. First order optimality conditions are rigorously derived and it is shown via formally matched asymptotic expansions that these conditions converge to classical first order conditions obtained in the context of shape calculus. We also discuss how to deal with triple junctions where e.g. two materials and the void meet. Finally, we present several numerical results for mean compliance problems and a cost involving the least square error to a target displacement

An Adaptive Phase-Field Method for Structural Topology Optimization

In this work, we develop an adaptive algorithm for the efficient numerical solution of the minimum compliance problem in topology optimization. The algorithm employs the phase field approximation and continuous density field. The adaptive procedure is driven by two residual type a posteriori error estimators, one for the state variable and the other for the objective functional. The adaptive algorithm is provably convergent in the sense that the sequence of numerical approximations generated by the adaptive algorithm contains a subsequence convergent to a solution of the continuous first-order optimality system. We provide several numerical simulations to show the distinct features of the algorithm.Comment: 30 pages, 10 figure

Structural Topology Optimization with Stress Constraint Considering Loading Uncertainties

This paper deals with the consideration of loading uncertainties in topology optimization via a fundamental optimization problem setting. Variability of loading in engineering design is realized e.g. in the action of various load combinations. In this study this phenomenon is modelled by the application of two mutually excluding (i.e. alternating) forces such that the magnitudes and directions are varied parametrically in a range. The optimization problem is stated as to find the minimum volume (i.e. the minimum weight) load-bearing elastic truss structure that transfers such loads acting at a fix point of application to a given line of support provided that stress limits are set. The aim of this paper is to numerically determine the layout, size, and volume of the optimal truss and to support the numerical results by appropriate analytical derivations. We also show that the optimum solution is non-unique, which aects the static determinacy of the structure as well. In this paper we also create a truss-like structure with rigid connections based on the results of the truss optimization and analyse it both as a bar structure (frame model) and a planar continuum (disk) structure to compare with the truss model. The comparative investigation assesses the validity of computational models and proves that the choice aects design negatively since rigidity of connections resulted by usual construction technologies involve extra stresses leading to significant undersizing

An Algorithm for Structural Topology Optimization of Multibody Systems

Topology Optimization (TO) of static structures with fixed loading is a very interesting topic in structural mechanics that has found many applications in industrial design tasks. The extension of the theory to dynamic loading for designing a Multibody System (MBS) with bodies which are lighter and stronger can be of high interest. The objective of this thesis work is to investigate one of the possible ways of extending the theory of the static structural Topology Optimization to Topology Optimization of dynamical bodies embedded in a Multibody System (TOMBS) with large rotational and transitional motion. The TOMBS is performed for all flexible bodies simultaneously based on the overall system dynamical response. Simulation of the MBS behavior is done using the finite element formalism and modal reduction. A modified formulation of Solid Isometric Material with Penalization (SIMP) method is suggested to avoid numerical instabilities and non-convergence of the optimization algorithm implemented for TOMBS. The nonlinear differential algebraic equation of motion is solved numerically using Backward Differential Formula (BDF) with variable step size in SundialsTB and Assimulo integrators implemented in Matlab and Python. The approach can find many applications in designing vehicle systems, high speed robotic manipulators, airplanes and space structures. Also, to show the current capability of the tools in the industry to design a body under dynamic loading using the multiple static load cases, the lower A-arm of double wishbone suspension system is designed in Abaqus/TOSCA, where, the loads are collected from rigid multibody simulation in Dymola.In everyday life, people deal with different kinds of mechanical machines and mechanisms. These mechanisms are a set of mechanical and electrical parts designed to perform a specific task. Among the others, the task of a mechanical part is to carry a load or transfer it. The key question a designer should ask is how to design the part in terms of the shape, material, weight, etc. in order for the part to be optimal. This is a question that can be answered using structural optimization. Particularly in this thesis work it is tried to suggest an algorithm for optimizing the shape or material distribution of the parts within a multibody system. The method is called topology optimization of multibody system. The behavior of the system as a whole is considered to design each individual mechanical part

A Constraint Handling Strategy for Bit-Array Representation GA in Structural Topology Optimization

In this study, an improved bit-array representation method for structural topology optimization using the Genetic Algorithm (GA) is proposed. The issue of representation degeneracy is fully addressed and the importance of structural connectivity in a design is further emphasized. To evaluate the constrained objective function, Deb's constraint handling approach is further developed to ensure that feasible individuals are always better than infeasible ones in the population to improve the efficiency of the GA. A hierarchical violation penalty method is proposed to drive the GA search towards the topologies with higher structural performance, less unusable material and fewer separate objects in the design domain in a hierarchical manner. Numerical results of structural topology optimization problems of minimum weight and minimum compliance designs show the success of this novel bit-array representation method and suggest that the GA performance can be significantly improved by handling the design connectivity properly.Singapore-MIT Alliance (SMA