A novel density-based topology optimization framework for plastic energy absorbing structural designs with maximum damage constraint is proposed. This framework enables topologies to absorb large amount of energy via plastic work before failure occurs. To account for the plasticity and damage during the energy absorption, a coupled elastoplastic ductile damage model is incorporated with topology optimization. Appropriate material interpolation schemes are proposed to relax the damage in the low-density regions while still ensuring the convergence of Newton-Raphson solution process in the nonlinear finite element analyses. An effective method for obtaining path-dependent sensitivities of the plastic work and maximum damage via adjoint method is presented, and the sensitivities are verified by the central difference method. The effectiveness of the proposed methodology is demonstrated through a series of numerical examples.to the recent review studies [12,14]. Among these available methods, the density-based method is perhaps the most popular one, which is also the subject of this study.Most of the studies concerning density-based topology optimization are based on linear or nonlinear elastic material, with applications to stiffness designs, compliant mechanisms, and fundamental frequency designs [10,13,[22][23][24][25]. Energy absorption is an irreversible process and is accompanied by various inelastic material dependent mechanisms. To account for such inelastic material response, inelastic constitutive models should be considered in topology optimization for designing energy absorbing structures. However, there are limited studies in topology optimization considering material nonlinearities. An attempt to include von Mises elastoplasticity in topology optimization was first made by Swan and Kosaka [26], wherein interpolation schemes based on Voigt-Reuss type mixing rules were used. Maute et al. [27] and Schwarz et al.[28] considered a Solid Isotropic Material with Penalization (SIMP)-like interpolation [29] with von Mises plasticity for maximizing ductility in topology optimization and an approximate sensitivity analysis was utilized. Later on, Bogomolny and Amir [30] combined the Drucker-Prager elastoplasticity with topology optimization for conceptual maximum stiffness reinforced concrete structure designs and the adjoint method proposed by Michaleris et al. [31] was used for the sensitivity analysis. Kato et al. [32] eliminated the simplifications used in references [27,28] to obtain more accurate analytical sensitivities for multiphase material topology optimization with von Mises elastoplasticity. Nakshatrala and Tortorelli [33] proposed a topology optimization framework for energy dissipation maximization subjected to impact loadings wherein the material response was modeled with von Mises plasticity. Wallin et al. [34] extended the von Mises plasticity to finite strain scenario for maximum plastic work designs. Recently, the authors also incorporated anisotropic Hoffmann plasticity model in topology o...

No abstract

An adjoint sensitivity analysis framework to evaluate path-dependent design sensitivities for problems involving inelastic materials and dynamic effects is presented and shown in the context of topology optimization. The overall aim is to present a framework that unifies the sensitivity analyses existing in the literature and provides clear guidelines on how to formulate sensitivity analysis for a wide range of path-dependent system behaviors simulated using finite element analysis (FEA). In particular, the focus is on the identification of proper independent variables for constraint formulation, the overall structure of constraint derivatives arising from discrete FEA equations, and the consistent implementation of sensitivity analysis for diverse problem types. This framework is used to compute sensitivity values for a number of complex problems formulated within FEA for which sensitivity calculations are not available in the literature. The sensitivity values obtained are then rigorously verified using numerical differentiation based on the central-difference method. Problem types include the use of enhanced assumed strain elements, plane-stress constraints, nonlocal elastoplastic-damage formulations, kinematic/isotropic hardening, rate-dependent materials, finite deformations, and dynamics. Finally, topology optimization is carried out using some of the different problem types. KEYWORDSadjoint method, dynamical systems, nonlinear transient systems, path-dependent design sensitivity, topology optimization Int J Numer Methods Eng. 2018;115:1-56. wileyonlinelibrary.com/journal/nme

No abstract

Summary This paper focuses on topology optimization utilizing incompressible materials under both small‐ and finite‐deformation kinematics. To avoid the volumetric locking that accompanies incompressibility, linear and nonlinear mixed displacement/pressure (u/p) elements are utilized. A number of material interpolation schemes are compared, and a new scheme interpolating both Young's modulus and Poisson's ratio (E‐ν interpolation) is proposed. The efficacy of this proposed scheme is demonstrated on a number of examples under both small‐ and finite‐deformation kinematics. Excessive mesh distortions that may occur under finite deformations are dealt with by extending a linear energy interpolation approach to the nonlinear u/p formulation and utilizing an adaptive update strategy. The proposed optimization framework is demonstrated to be effective through a number of representative examples.