An immersed boundary approach for shape and topology optimization of stationary fluid-structure interaction problems
An immersed boundary approach for shape and topology optimization of stationary fluid-structure interaction problems
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DOI：
10.1007/s00158-016-1467-5
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发表时间：
2016-11
影响因子：
3.9
通讯作者：
N. Jenkins;K. Maute
中科院分区：
文献类型：
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作者：
N. Jenkins;K. Maute
提出了一种稳态流固耦合(FSI)问题的形状和拓扑优化方法。整个方法建立在浸没边界方法的基础上，该方法将结构的拉格朗日公式耦合到欧拉流体模型，并在变形网格上离散。通过改变离散化水平集场的节点参数来操纵流体-结构边界的几何形状。这种方法允许流体-结构界面的拓扑变化，但在优化过程中可能会出现固体材料的自由浮动体积。在FSI分析中，自由浮动体积被跟踪并建模为流体。为了感觉孤立的固体体积，在分析设计的FSI响应之前，计算由线性各向同性扩散描述的指示场。流体模型采用不可压缩的N-S方程，结构假定为线弹性。FSI模型采用扩展有限元方法离散，流固耦合条件被弱化。所得到的非线性方程组采用牛顿法进行整体求解。设计灵敏度用伴随法计算，优化问题用基于梯度的算法求解。以二维稳态问题为例，研究了该优化框架的特点。数值结果表明，所提出的处理自由漂浮体的方法在设计演化中引入了不连续性，但该方法仍然成功地收敛到有意义的设计。
This paper presents an approach to shape and topology optimization of fluid-structure interaction (FSI) problems at steady state. The overall approach builds on an immersed boundary method that couples a Lagrangian formulation of the structure to an Eulerian fluid model, discretized on a deforming mesh. The geometry of the fluid-structure boundary is manipulated by varying the nodal parameters of a discretized level set field. This approach allows for topological changes of the fluid-structure interface, but free-floating volumes of solid material can emerge in the course of the optimization process. The free-floating volumes are tracked and modeled as fluid in the FSI analysis. To sense the isolated solid volumes, an indicator field described by linear, isotropic diffusion is computed prior to analyzing the FSI response of a design. The fluid is modeled with the incompressible Navier-Stokes equations, and the structure is assumed linear elastic. The FSI model is discretized by an extended finite element method, and the fluid-structure coupling conditions are enforced weakly. The resulting nonlinear system of equations is solved monolithically with Newton’s method. The design sensitivities are computed by the adjoint method and the optimization problem is solved by a gradient-based algorithm. The characteristics of this optimization framework are studied with two-dimensional problems at steady state. Numerical results indicate that the proposed treatment of free-floating volumes introduces a discontinuity in the design evolution, yet the method is still successful in converging to meaningful designs.