Title: An error-in-constitutive equations strategy for topology optimization for frequency-domain dynamics

Abstract

This paper presents a topology optimization formulation for frequency-domain dynamics to reduce solution dependence upon initial guess and considered loading conditions. Due to resonance phenomena in undamped steady-state dynamics, objectives measuring dynamic response possess many local minima that may represent poor solutions to a design problem, an issue exacerbated for design with respect to multiple frequencies. In this work, we propose an extension of the modified error-in-constitutive-equations (MECE) method, used previously in material identification inverse problems, as a new approach for frequency-domain dynamics topology optimization to mitigate these issues. The main idea of the proposed framework is to incorporate an additional penalty-like term in the objective function that measures the discrepancy in the constitutive relations between stresses and strains and between inertial forces and displacements. Then, the design problem is cast within a PDE-constrained optimization formulation in which we seek displacements, stresses, inertial forces, and a density-field solution that minimize our new objective subject to conservation of linear momentum plus some additional constraints. We show that this approach yields superior designs to conventional gradient-based optimization approaches that solely use a functional of displacements as the objective, while strictly enforcing the constitutive equations. The MECE strategy integrates into a density-based topologymore » optimization scheme for void–solid or two-phase material structural design. We highlight the merits of our approach in a variety of scenarios for direct frequency response design, considering multiple frequency load cases and structural objectives.« less

Authors:

Sanders, Clay ^[1]; Norato, Julián ^[2]; Walsh, Timothy ^[3]; Aquino, Wilkins ^[1]

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+ Show Author Affiliations

1. Duke Univ., Durham, NC (United States)
2. Univ. of Connecticut, Storrs, CT (United States)
3. Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

Publication Date:

Mon Sep 28 00:00:00 EDT 2020

Research Org.:

Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

Sponsoring Org.:

USDOE National Nuclear Security Administration (NNSA)

OSTI Identifier:

1668695

Alternate Identifier(s):

OSTI ID: 1809314

Report Number(s):

SAND-2019-10373J
Journal ID: ISSN 0045-7825; 679039

Grant/Contract Number:  

AC04-94AL85000; NA0003525; FG02-97ER25308

Resource Type:

Accepted Manuscript

Journal Name:

Computer Methods in Applied Mechanics and Engineering

Additional Journal Information:

Journal Volume: 372; Journal ID: ISSN 0045-7825

Publisher:

Elsevier

Country of Publication:

United States

Language:

English

Subject:

42 ENGINEERING; Topology optimization; dynamic response design; PDE-constrained optimization; error in constitutive equations; vibration reduction