The present paper deals with the development of a Galerkin Boundary Element Method (Galerkin-BEM) approach applied to the numerical simulation of plane and half-plane quasi-static viscoelastic problems. This approach makes use of a half-plane viscoelastic fundamental solution, thus avoiding the full discretization of the half-plane and consequently reducing the computational requirements of the proposed model. Time-domain responses are obtained by means of the viscoelastic reciprocal theorem and its temporal integrations are evaluated by using the Stieltjes convolutions. Numerical simulations are carried out in order to assess the accuracy and the applicability of the proposed approach to viscoelastic problems by comparing its results with those provided by the numerical and analytical solutions reported in the literature.

本文讨论了应用于平面和半平面准静态粘弹性问题的数值模拟的 Galerkin 边界元方法 (Galerkin-BEM) 方法的发展。这种方法利用了半平面粘弹性基本解，从而避免了半平面的完全离散化，从而减少了所提出模型的计算要求。时域响应是通过粘弹性互易定理获得的，其时间积分是通过使用 Stieltjes 卷积来评估的。进行数值模拟是为了通过将其结果与文献中报道的数值和解析解提供的结果进行比较来评估所提出的方法对粘弹性问题的准确性和适用性。