基于optimization的周向-有限元耦合和非局部边界条件规定策略
An optimization-based strategy for peridynamic-FEM coupling and for the prescription of nonlocal boundary conditions
摘要：
我们开发和分析了一个基于优化的方法耦合的静态围动力（PD）模型和静态经典弹性模型。该方法制定的耦合作为一个控制问题，其中的状态是PD和经典方程的解决方案，其目标是尽量减少他们的不匹配的PD和经典域的重叠，和控制的虚拟体积约束和边界条件施加在本地-非本地接口。我们的三维几何形状的数值试验表明，我们的方法，其数值收敛性，其适用性，以现实的工程几何形状的一致性和准确性。我们证明了耦合策略作为一种手段，以减少计算费用，限制非局部模型的一个子域的利益，并作为一种手段，以传输本地（例如，牵引）边界条件应用在表面上的非局部模型的大部分领域。
英文摘要：
We develop and analyze an optimization-based method for the coupling of a static peri-dynamic (PD) model and a static classical elasticity model. The approach formulates the coupling as a control problem in which the states are the solutions of the PD and classical equations, the objective is to minimize their mismatch on an overlap of the PD and classical domains, and the controls are virtual volume constraints and boundary conditions applied at the local-nonlocal interface. Our numerical tests performed on three-dimensional geometries illustrate the consistency and accuracy of our method, its numerical convergence, and its applicability to realistic engineering geometries. We demonstrate the coupling strategy as a means to reduce computational expense by confining the nonlocal model to a subdomain of interest, and as a means to transmit local (e.g., traction) boundary conditions applied at a surface to a nonlocal model in the bulk of the domain.
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