Shape preserving design of geometrically nonlinear structures using topology optimization

Abstract

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Shape preserving design of thermo-elastic structures considering geometrical nonlinearity

“…As illustrated in Figure 2, sub-regions are defined as shape preserving domains Ω s , where local warping deformations under mechanical and heat loads are concerned. Based on the previous work [28] in a pure mechanical loading case, the shape preserving design of thermo-elastic structures can be further developed by incorporating the thermo-elastic analysis as stated in Sec. 2.1 into the optimization system.…”

“…The thermal field is a design-dependent temperature result of steady-state heat conduction. Furthermore, a shape preserving design [26][27][28] of thermoelastic structures is considered to eliminate local warping deformation caused by the thermal stress and then to maintain the normal operation. Until now, shape preserving design has only been developed in pure mechanical situations.…”

A density‐based boundary evolving method for buckling‐induced design under large deformation

“…(The initial point of Newton-Raphson method is obtained through MGDCM algorithm). Once the solutions are obtained, the objective and constraint functions are computed using Equation 29, and sensitivity analysis 1 and 2 are conducted as described in Equation (39)- (40). Note that the chain rule should be used to compute the sensitivity with respect to design variables described in Section 2.3.…”

“…Ivarsson et al 39 applied a transient finite strain viscoplastic model in gradient‐based TO framework to design impact mitigating structures. Li et al 40 extended the shape‐preserving TO approach from linear elastic case to geometrically nonlinear problems, where the structural complementary elastic work is chosen as objective function. Luo et al 41 proposed a simple and effective additive hyperelasticity technique to circumvent excessive mesh distortion in solving the density‐based TO of elastic structures undergoing large deformation.…”

A new geometrically nonlinear topology optimization formulation for controlling maximum displacement

“…To take advantage of Ansys, the neo-Hookean and second-order Yeoh models were utilized to circumvent the numerical instabilities. Li et al (2019) extended the shape-preserving topology optimization method to solve geometrically nonlinear problems, in which a novel warping index was proposed. Besides the FE analysis, the geometrically nonlinear topology optimization in the framework of the mesh-free method is carried out to resolve numerical difficulties (Cho and Kwak 2006;He, Zhan, and Wang 2014;Zheng, Yang, and Long 2015).…”