The paper presents the approach for solving 2D elastic boundary value problems defined in domains with inclusions with different material properties using the parametric integral equation system (PIES). The main feature of the proposed strategy is using Bézier surfaces for global modeling of inclusions. Polygonal inclusions are defined by bilinear surfaces, while others by bicubic surfaces. It is beneficial over other numerical methods (such as FEM and BEM) due to the lack of discretization. Integration over inclusions defined by surfaces is also performed globally without division into subareas. The considered problem is solved iteratively in order to simulate different material properties by applying initial stresses within the inclusion. This way of solving avoids increasing the number of unknowns and can also be used for elasto-plastic problems without significant changes. Some numerical tests are presented, in which the results obtained are compared with those calculated by other numerical methods. This paper is an extended version of author's conference paper [1]. It has been enriched with, among others, the description of modeling more complex inclusions, as well as additional results obtained by PIES compared to other numerical methods.

本文提出了一种使用参数积分方程组（PIES）解决具有不同材料属性的夹杂物的二维弹性边界值问题的方法。提出的策略的主要特征是使用Bézier曲面对夹杂物进行整体建模。多边形夹杂物是由双线性曲面定义的，而其他夹杂物是由双三次曲面定义的。由于没有离散化，它比其他数值方法（例如FEM和BEM）有益。由表面定义的内含物的积分也可以全局执行，而无需划分为子区域。迭代解决所考虑的问题，以便通过在夹杂物中施加初始应力来模拟不同的材料特性。这种解决方式避免了未知数的增加，并且还可以用于弹塑性问题而无需进行重大更改。提出了一些数值测试，其中将获得的结果与通过其他数值方法计算得到的结果进行比较。本文是作者会议论文的扩展版[1]。它尤其丰富了对更复杂的包含物进行建模的描述，以及与其他数值方法相比通过PIES获得的其他结果。