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Boundary element method for contact between multiple rigid punches and anisotropic viscoelastic foundation

机译：多个刚性冲孔与各向异性粘弹性基础接触的边界元法

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摘要

In this paper both of the elastic-viscoelastic correspondence principle and time stepping method, which can convert viscoelasticity to elasticity, are employed to the boundary element method (BEM) to solve the contact problems between multiple rigid punches and anisotropic viscoelastic foundation. The one based upon the correspondence principle has the restriction on time-invariant boundaries, and hence can only be applied to the cases of complete indentation whose contact region as well as contact status are time-independent. The other based upon the time stepping method is processed step-by-step in time domain, and its boundary conditions may vary in each time step, and hence can be applied to both complete and incomplete indentations. Both methods are valid for the frictionless or frictional contact surface, the punches can be in equilibrium status or in quasi-static sliding condition, and the number of punches and the punch profiles are arbitrary. Benefited by the elastic system used for BEM, both methods hold the feature that no meshes are required on the rigid punches and holes/cracks. Through the iteration procedure and numerical examples presented in this study, we see that the one based upon time-stepping method is much more general and efficient than the other one.
机译：在本文中，两种弹性粘弹性原理和时间步进方法都可以将粘弹性转化为弹性，用于解决边界元素方法（BEM），以解决多个刚性冲孔和各向异性粘弹性基础之间的接触问题。基于对应原理的彼此具有限制时间不变边界，因此只能应用于其接触区域以及接触状态的完整压痕的情况是时间无关的。基于时间梯度方法的另一个在时域的逐步处理，并且其边界条件可以在每个时间步骤中变化，因此可以应用于完整和不完整的凹进。两种方法对于无摩擦或摩擦接触表面有效，冲头可以处于平衡状态或以准静态滑动条件，以及冲头的数量和冲头轮廓是任意的。由用于BEM的弹性系统受益，两种方法都保持了刚性冲头和孔/裂缝上不需要网格的特征。通过本研究中呈现的迭代程序和数值示例，我们看到基于时间级步骤方法比另一个更通用和有效。

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