Form Finding of Sparse Structures with Continuum Topology Optimization

Abstract

A continuum topology optimization methodology suitable for finding optimal forms of large-scale sparse structures is presented. Since the need to avoid long compressive spans can be critical in determining the optimal form of such structures, a formulation is used wherein the structure is modeled as a linear elastic continuum subjected to design loads, and optimized in form to maximize the minimum critical buckling load. Numerical issues pertinent to accurate solution of the linearized buckling eigenvalue problem and accurate design sensitivity analysis are discussed. The performance of the proposed design formulation is demonstrated on a few problems designed to find optimal forms of a canyon bridge, long-span bridges, and an electrical transmission tower. In all cases, very credible structural forms are obtained with the proposed design formulation. The results of the design examples solved are typically superior structural forms with regard to buckling stability than those obtained to minimize the mean structural compliance.

Structural topology optimization of vibrating structures with specified eigenfrequencies and eigenmode shapes

“…, n) are selected and evaluated independently of the shape functions for displacement fields. Also note that similar formulations based on the SIMP method were presented by Rahmatalla and Swan [42,43]. Although they pointed out some numerical problems such as 'layering' and 'islanding' using coarse meshes [43], the numerical examples obtained by the method proposed here will show clear optimal configurations, without the above problems.…”

“…Equation (43) implies that we can quickly obtain sensitivities of eigenmodes by solving just the equilibrium equation, Equation (42). This is a great advantage for the current formulation of the objective function concerning the eigenmodes.…”

Robust Topology Optimization for Compliant Mechanisms Considering Uncertainty of Applied Loads

“…with the direction of the variable load σ t 1 that is defined as being perpendicular to the average load in Eq. (21). Consequently, Eq.…”

Structural Topology Optimization: Moving Beyond Linear Elastic Design Objectives

“…As a first step, several researchers have proposed using linearized eigenstability metrics for optimizing structural stiffness (see e.g., Rahmatalla and Swan, 2003). Formal incorporation of geometric and/or material nonlinearities requires iterative analysis and a constraint on the residual R of equilibrium equations.…”