Design of dissipative multimaterial viscoelastic‐hyperelastic systems at finite strains via topology optimization

Abstract

Summary This study focuses on the topology optimization framework for the design of multimaterial dissipative systems at finite strains. The overall goal is to combine a soft viscoelastic material with a stiff hyperelastic material for realizing optimal structural designs with tailored damping and stiffness characteristics. To this end, several challenges associated with incorporating finite‐deformation viscoelastic‐hyperelastic materials in a multimaterial design framework are addressed. This includes consideration of a thermodynamically consistent finite‐strain viscoelasticity model for simulating energy dissipation together with F‐bar finite elements for handling material incompressibility. Moreover, an effective multimaterial interpolation scheme is proposed, which preserves the physics of material mixtures in the context of density‐based topology optimization. A numerically accurate analytical design sensitivity calculation is also presented using a path‐dependent adjoint method. Furthermore, both prescribed‐load and prescribed‐displacement boundary conditions are considered in the optimization formulations, together with various strategies for controlling stiffness. As demonstrated by the numerical examples, the use of the stiffer hyperelastic material phase in a design not only improves stiffness but also increases energy dissipation capacity. Moreover, with the finite‐deformation theory, the effect of the loading magnitude on the optimized designs can be observed.

Damping optimization of viscoelastic cantilever beams and plates under free vibration

“…Elsabbagh and Baz [16] conducted the topology optimization of unconstrained layer damping (UCLD) treatments, optimizing the distribution of the viscoelastic treatment. Zhang and Khandelwal [38] proposed the topology optimization of multimaterial dissipative systems at finite strains. More specifically, the popular solid isotropic material with penalization (SIMP) method is considered in a number of works.…”

Geotechnical Characteristic Assessments of Floodplain Soils Using SCPTU Data in Nanjing, China

“…This study focuses on the topology optimization of structures with minimized end compliance while satisfying material volume and nonlinear stability constraints. The main contributions of this work are: (a) A novel strategy for removing spurious buckling modes based on the construction of a pseudo-mass matrix is proposed; (b) A new formulation of nonlinear stability analysis in topology optimization is considered by directly computing the eigenvalues of the tangent stiffness matrix where no other approximations are made; (c) The optimization problem is formulated to incorporate a fixed number of clusters of eigenvalues rather than a fixed number of eigenvalues so that it can handle arbitrary multiplicities of eigenvalues during the optimization process; (d) the adaptive linear energy interpolation proposed in Zhang et al [16] which has shown robust performance in handling mesh distortions in the previous studies [13,43,44] is incorporated in the proposed framework; and (e) Finally, the post-analysis on the B-spline fitted optimized topologies is carried out to evaluated the stability performance of the optimized structures.…”

Topology optimization employing a condensation method for nonlinear structural frames with supplemental mass

“…Researchers have suggested various schemas to consider material nonlinearity in topology optimization for quasi‐static loading from early developments based on elastoplacticity, 10‐12 to more recent extensions considering plasticity methods 13‐17 . However, for dynamic excitation, challenges corresponding to the optimization methods arise from the time‐varying nature of the external forces that complicates the analysis for response evaluation and gradient expressions at each iteration of optimization 18‐21 .…”

“…Researchers have suggested various schemas to consider material nonlinearity in topology optimization for quasi-static loading from early developments based on elastoplacticity, [10][11][12] to more recent extensions considering plasticity methods. [13][14][15][16][17] However, for dynamic excitation, challenges corresponding to the optimization methods arise from the time-varying nature of the external forces that complicates the analysis for response evaluation and gradient expressions at each iteration of optimization. [18][19][20][21] Although some studies have relaxed the linear material assumption for dynamic excitation in topology optimization, [22][23][24][25] in these studies, nonlinearity is considered through plasticity formulations, and a Newton type scheme is employed to iteratively update the stiffness matrix, at each time-step, due to the nonconstant stiffness matrix until convergence of a residual.…”