An Iterative Thresholding Method for the Minimum Compliance Problem

In this paper,we propose a simple energy decaying iterative thresholding algorithm to solve the two-phase minimum compliance problem.The material domain is implicitly represented by its characteristic function,and the problem is formulated into a minimization problem by the principle of minimum complementary energy.We prove that the energy is decreasing in each iteration.Two effective continuation schemes are proposed to avoid trapping into the local minimum.Numerical results on 2D isotropic linear material demonstrate the effectiveness of the proposed methods.

Topology optimization of shear wall structures under seismic loading

A topology optimization formulation is developed to find the stiffest structure with desirable material distribution subjected to seismic loads. Finite element models of the structures are generated and the optimality criteria method is modified using a simple penalty approach and introducing fictitious strain energy to simultaneously consider both material volume and displacement constraints. Different types of shear walls with/without opening are investigated. Additionally, the effects of shear wall-frame interaction for single and coupled shear walls are studied. Gravity and seismic loads are applied to the shear walls so that the definitions provide a practical approach for locating the critical parts of these structures. The results suggest new viewpoints for architectural and structural engineering for placement of openings.

Thermoelastic Structural Topology Optimization Based on Moving Morphable Components Framework

This study investigates structural topology optimization of thermoelastic structures considering two kinds of objectives ofminimumstructural compliance and elastic strain energy with a specified available volume constraint.To explicitly express the configuration evolution in the structural topology optimization under combination of mechanical and thermal load conditions,the moving morphable components(MMC)framework is adopted.Based on the characteristics of the MMC framework,the number of design variables can be reduced substantially.Corresponding optimization formulation in the MMC topology optimization framework and numerical solution procedures are developed for several numerical examples.Different optimization results are obtained with structural compliance and elastic strain energy as objectives,respectively,for thermoelastic problems.The effectiveness of the proposed optimization formulation is validated by the numerical examples.It is revealed that for the optimization design of the thermoelastic structural strength,the objective function with the minimum structural strain energy can achieve a better performance than that from structural compliance design.

structures:new solutions and uncommon characteristics James Kirby,Shiwei Zhou,

To investigate the characteristics of optimal fail-safe structures subjected to single and multi-member damage scenarios,we con-sider a pin-jointed cantilever truss with all members directly connected from the load point to the boundary.Two problem formu-lations are considered—minimizing the compliance with a volume constraint and minimizing the volume with stress constraints.Whilst these formulations produce equivalent structures for traditional truss design problems,we find that this is not always the case in the fail-safe setting.Analytical solutions are developed for a three-bar truss under both problem formulations.Damage is modelled as the complete removal of any one member,and a minmax problem is constructed to minimize the compliance or volume of the structure for the worst-case damage scenario.These new analytical solutions provide much needed benchmarks for numerical fail-safe methods.The problems are extended to n-bar systems with damage to multiple members.Results show that as the structural complexity(the number of members in a system)increases,the optimum fail-safe structure tends towards a variation of the nominal two-bar design with overlapping members.From these observations,we then approach the idea of full redundancy through the introduction of parallel substructures into a more complex truss design.We compare our fully redundant truss design with a benchmark fail-safe solution and show that the fully redundant design has significantly better performance and with fewer members.Practically,this suggests that fully redundant structural designs are highly efficient and have the additional benefit of only requiring the computation of the nominal solution.