A new geometrically nonlinear topology optimization formulation for controlling maximum displacement

Abstract

This article presents a novel formulation for geometric nonlinear topology optimization problems. In practical engineering, maximum deflection is frequently used to quantify the stiffness of continuum structures, yet not applied generally as the optimization constraint in geometrically nonlinear topology optimization problems. In this study, the maximum nodal displacement is formulated as a sole constraint. The p-mean aggregation function is adopted to efficiently treat a mass of local displacement constraints imposed on nodes in the user-specified region. The sensitivities of the objective and constraint functions with respect to relative densities are derived. The effect of the aggregate parameter on the final design is further investigated through numerical examples. By comparison with final designs from the traditional formulation, i.e. minimization end compliance with the volume fraction constraint, or minimization of total volume subject to multiple nodal displacement constraints, the optimized results clearly demonstrate the necessity for and efficiency of the present approach.

An Overview of Sequential Approximation in Topology Optimization of Continuum Structure

“…In addition, the MMA algorithm is also used as the optimizer in various topology optimization methods, such as the stiffness spreading method [55][56][57], parameterized level-set method [58], an approach driven by MMC and moving morphable bars [59][60][61], series-expansion framework [62][63][64], the iso-geometric based method [65]. In addition to the compliance minimization problem, MMA is also applied to various non-self-adjoint problems, such as stress-constrained problems [66,67], fiber orientation optimization problems [68], transient excited and geometrically nonlinear structures [69,70], transient heat conduction [71], fail-safe design [72]. Among them, the default parameters may be different, and some numerical skills and experience are required for some particular methodologies or problems.…”

Nonlinear topology optimization design and gripping tests of a novel origami chomper-based flexible gripper

“…Considering the considerable deformation characteristics of the flexible robot grippers, the linear assumptions may make the designs inaccurate or underperforming. Therefore, this study attempts to use nonlinear topology optimization methods [58][59][60][61][62][63][64][65][66] to more accurately upgrade the origami grippers' performance.…”

Origami Chomper‐Based Flexible Gripper with Superior Gripping Performances

“…Considering the considerable deformation characteristics of flexible robot grippers, linear assumptions may result in inaccurate or underperforming designs. Therefore, this study attempted to use nonlinear topology optimization (NTO) methods [59][60][61][62][63][64][65][66][67] to improve the performance of origami grippers more accurately. Considering the refinement design requirements of origami grippers and computationally costly NTO, we adopted a multiresolution strategy in the NTO.…”