A novel approach of reliability-based topology optimization for continuum structures under interval uncertainties

Abstract

Purpose The purpose of this paper is to propose a novel non-probabilistic reliability-based topology optimization (NRBTO) method for continuum structural design under interval uncertainties of load and material parameters based on the technology of 3D printing or additive manufacturing. Design/methodology/approach First, the uncertainty quantification analysis is accomplished by interval Taylor extension to determine boundary rules of concerned displacement responses. Based on the interval interference theory, a novel reliability index, named as the optimization feature distance, is then introduced to construct non-probabilistic reliability constraints. To circumvent convergence difficulties in solving large-scale variable optimization problems, the gradient-based method of moving asymptotes is also used, in which the sensitivity expressions of the present reliability measurements with respect to design variables are deduced by combination of the adjoint vector scheme and interval mathematics. Findings The main findings of this paper should lie in that new non-probabilistic reliability index, i.e. the optimization feature distance which is defined and further incorporated in continuum topology optimization issues. Besides, a novel concurrent design strategy under consideration of macro-micro integration is presented by using the developed RBTO methodology. Originality/value Uncertainty propagation analysis based on the interval Taylor extension method is conducted. Novel reliability index of the optimization feature distance is defined. Expressions of the adjoint vectors between interval bounds of displacement responses and the relative density are deduced. New NRBTO method subjected to continuum structures is developed and further solved by MMA algorithms.

Two decades review of reliability-based topology optimization developments

“…After that, Wang et al (2019a) developed a new RBTO framework for the concurrent design of solid and truss-like material structures with unknown but bounded uncertainties. In the same period, Wang et al (2019b) developed an RBTO approach for continuum structures under interval uncertainties. And Wang et al (2019c) developed a non-probabilistic RBTO approach for multi-material layout design via interval and convex mixed uncertainties.…”

Topology Optimisation in Structural Steel Design for Additive Manufacturing

“…[571] A Non-Probabilistic Reliability-Based Topology Optimisation (NRBTO) method to account for additively manufactured materials' properties uncertainty. [572] A TO method to account for AM cost and fabrication time.…”