Level set topology optimization of structural problems with interface cohesion

Behrou, Reza; Lawry, Matthew; Maute, Kurt

doi:10.1002/nme.5540

Level set topology optimization of structural problems with interface cohesion

Journal Article · Fri Mar 17 00:00:00 EDT 2017 · International Journal for Numerical Methods in Engineering

DOI:https://doi.org/10.1002/nme.5540· OSTI ID:1401074

^[1]; Lawry, Matthew ^[2]; Maute, Kurt ^[2]

Department of Civil, Environmental and Architectural Engineering University of Colorado Boulder Boulder 80309‐0428 CO USA
Department of Aerospace Engineering University of Colorado Boulder Boulder 80309‐0429 CO USA

Summary

This paper presents a finite element topology optimization framework for the design of two‐phase structural systems considering contact and cohesion phenomena along the interface. The geometry of the material interface is described by an explicit level set method, and the structural response is predicted by the extended finite element method. In this work, the interface condition is described by a bilinear cohesive zone model on the basis of the traction‐separation constitutive relation. The non‐penetration condition in the presence of compressive interface forces is enforced by a stabilized Lagrange multiplier method. The mechanical model assumes a linear elastic isotropic material, infinitesimal strain theory, and a quasi‐static response. The optimization problem is solved by a nonlinear programming method, and the design sensitivities are computed by the adjoint method. The performance of the presented method is evaluated by 2D and 3D numerical examples. The results obtained from topology optimization reveal distinct design characteristics for the various interface phenomena considered. In addition, 3D examples demonstrate optimal geometries that cannot be fully captured by reduced dimensionality. The optimization framework presented is limited to two‐phase structural systems where the material interface is coincident in the undeformed configuration, and to structural responses that remain valid considering small strain kinematics. Copyright © 2017 John Wiley & Sons, Ltd.

View Accepted Manuscript (Publisher)

Sponsoring Organization:: USDOE

OSTI ID:: 1401074

Journal Information:: International Journal for Numerical Methods in Engineering, Journal Name: International Journal for Numerical Methods in Engineering Journal Issue: 8 Vol. 112; ISSN 0029-5981

Publisher:: Wiley Blackwell (John Wiley & Sons)Copyright Statement

Country of Publication:: United Kingdom

Language:: English

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