Topology optimization with incompressible materials under small and finite deformations using mixed u/p elements
Topology optimization with incompressible materials under small and finite deformations using mixed u/p elements
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DOI：
10.1002/nme.5834
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发表时间：
2018-08
影响因子：
2.9
通讯作者：
Guodong Zhang;Ryan Alberdi;Kapil Khandelwal
中科院分区：
文献类型：
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作者：
Guodong Zhang;Ryan Alberdi;Kapil Khandelwal
本文的重点是在小变形和有限变形运动学下利用不可压缩材料的拓扑优化。为了避免伴随不可压缩性的体积锁定，使用了线性和非线性混合位移/压力（u/p）单元。比较了几种材料插值格式，提出了杨氏模量和泊松比插值的新格式（E‐ν插值）。在小变形和有限变形的情况下，通过一些实例证明了该方案的有效性。通过将线性能量插值方法扩展到非线性u/p公式并利用自适应更新策略来处理有限变形下可能出现的过度网格变形。通过若干具有代表性的算例验证了所提出的优化框架的有效性。
This paper focuses on topology optimization utilizing incompressible materials under both small‐ and finite‐deformation kinematics. To avoid the volumetric locking that accompanies incompressibility, linear and nonlinear mixed displacement/pressure (u/p) elements are utilized. A number of material interpolation schemes are compared, and a new scheme interpolating both Young's modulus and Poisson's ratio (E‐ν interpolation) is proposed. The efficacy of this proposed scheme is demonstrated on a number of examples under both small‐ and finite‐deformation kinematics. Excessive mesh distortions that may occur under finite deformations are dealt with by extending a linear energy interpolation approach to the nonlinear u/p formulation and utilizing an adaptive update strategy. The proposed optimization framework is demonstrated to be effective through a number of representative examples.