Abstract
The objective of this study is to develop an optimization methodology to find a layout that traces a prescribed force–displacement curve through a topology optimization approach. To this end, we propose an objective function to minimize the difference between a prescribed force–displacement curve and the curve calculated at each iteration of the optimization process. Slope constraints are introduced to solve issues encountered when using a small number of target points. In addition, a projection filter is employed to suppress the gray region observed between the solid and void regions, which generally occurs when using a density-based filter. A recently proposed energy interpolation scheme is implemented to stabilize the instability in the nonlinear analysis, which generally results from excessive distortion in the void region when the structure is modeled on a fixed mesh in the topology optimization process. To validate the outlined methodology, several case studies with different types of nonlinearity and structural features of the obtained layouts are investigated.
Highlights
The generalized Hook’s elasticity law is not valid if a structure undergoes large deformation, for which the force–displacement (F-D) curve exhibits nonlinear behavior due to geometric nonlinearity [1,2,3]
Buhl et al [5] dealt with an optimization problem concerning geometric nonlinearity due to large deformation, and many studies have since been introduced for topology optimization problems of mechanical structures associated with geometrically nonlinear modeling [6,7,8]
A topology optimization method has been proposed to find the layout of a structure that traces the prescribed nonlinearity on the F-D curve
Summary
The generalized Hook’s elasticity law is not valid if a structure undergoes large deformation, for which the force–displacement (F-D) curve exhibits nonlinear behavior due to geometric nonlinearity [1,2,3]. This study is organized as follows: In Section 2 the underlying theories are explained; in Section 2.1, we define the optimization problem and present the governing equations for a geometrically nonlinear finite element and sensitivity analysis for the objective function; in Section 2.2, we describe the density filter and parameterization for the energy interpolation; in Section 2.3, we describe concepts of the slope used in the optimization problem as a constraint and the sensitivity analysis; in Section 3, we demonstrate the performance of the proposed method using a thin plate; and, we present the conclusions. The topology optimization and optimal design in this study were basically constructed based on the 88 lines code [26]
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