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Mapped infinite p-element for two-dimensional problems of unbounded domains

机译：无限域的二维问题的映射无限p元素

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摘要

A new mapped infinite p-element is formulated for two-dimensional problems of unbounded domains. The shape functions along the infinite direction are constructed from the shifted Legendre orthogonal polynomials. The element is characterized by the simplicity of the mapping and the retention of standard integration abscissas and weights. The performance of the proposed mapped infinite p-element is assessed by solving a problem of an infinite medium with a circular opening loaded by internal pressure, a problem of a uniformly loaded circular area on the surface of an elastic half-space, and a case of an infinitely extended medium loaded by uniform pressure. A version of the axisymmetric problem with uniform load applied to a circular slab resting on the surface of an elastic half-space is also shown. Furthermore, comparisons on a d.o.f. basis are made with solutions from truncated finite element meshes. The numerical results show the efficiency of the proposed mapped infinite p-element.
机译：针对无界域的二维问题，制定了新的映射无限p元素。沿无限方向的形状函数由位移的Legendre正交多项式构造而成。该元素的特点是映射简单，并保留标准积分横坐标和权重。拟议的映射无限p元素的性能通过解决无限大介质的圆形开口受内部压力加载的问题，弹性半空间表面上均匀加载的圆形区域的问题以及情况来评估均匀压力加载的无限延伸介质的数量。还显示了轴对称问题的一种形式，其中均匀载荷施加到放置在弹性半空间表面上的圆形平板上。此外，在d.o.f.上进行比较截断有限元网格的解为基础。数值结果表明了所提出的映射无限p元素的效率。

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