Abstract For the accurate imposition of surface loads using the Finite Element Method normally the load is discretized at the surface facets. Therefore appropriate surface shape functions are needed. If the surface contains kinks, which occurs often in contact cases, the imposition is more complicated. In order to simplify the imposition of surface loads, an alternative approach is presented. This formulation is purely based on volume contributions of the discretized elements of the body. The surface nodes are automatically identified and the linearization is straightforward. No specific surface information is necessary. The imposition is simply based on the application of the divergence theorem. The only prerequisite is the fulfillment of the integration constraint, a necessary requirement for Galerkin solution schemes. With this, boundary nodes are directly identified by possessing a non zero normal vector whereas for inner nodes this vector is identically zero. Moreover, the normal vectors at the boundary nodes contain all the information of the surface and correspond to resultant nodal normal vectors. This is especially advantageous in the case of surfaces that contain kinks. It also simplifies the search algorithm in computational contact mechanics to find the closest distance to other bodies. This approach also works for any kind of shape functions. The nodal force vectors are always determined accurately. The advantages and the simple handling of this approach are demonstrated by means of several examples including follower loads and contact cases. Additionally, the influence of the isoparametric concept on the integration constraint is investigated by evaluating the behavior of different shape functions on an irregular grid. Although this new approach is only demonstrated within the context of the Finite Element Method, due to its generic derivation it can be applied to any Galerkin solution scheme which fulfills the integration constraint.

中文翻译：

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使用发散定理直接节点施加表面载荷

摘要 为了使用有限元方法精确施加表面载荷，载荷通常在表面小面上离散化。因此需要适当的表面形状函数。如果表面包含扭结（这在接触情况下经常发生），则拼版会更加复杂。为了简化表面载荷的施加，提出了一种替代方法。该公式完全基于主体离散元素的体积贡献。表面节点是自动识别的，线性化很简单。不需要特定的表面信息。强加只是基于散度定理的应用。唯一的先决条件是满足积分约束，这是 Galerkin 解决方案的必要条件。有了这个，边界节点通过拥有一个非零法向量直接识别，而对于内部节点，该向量完全为零。此外，边界节点处的法向量包含表面的所有信息，并对应于结果节点的法向量。这在包含扭结的表面的情况下尤其有利。它还简化了计算接触力学中的搜索算法，以找到与其他物体的最近距离。这种方法也适用于任何类型的形状函数。节点力矢量总是被准确地确定。这种方法的优点和简单的处理通过几个例子来证明，包括跟随负载和接触情况。此外，通过评估不同形状函数在不规则网格上的行为，研究了等参概念对积分约束的影响。尽管这种新方法仅在有限元方法的上下文中进行了演示，但由于其通用推导，它可以应用于满足积分约束的任何 Galerkin 解决方案方案。