The superellipsoids, part of the family of superquadratics, have geometric and mathematical properties that not only make them suitable for the representation of solids, ranging from spheres to relatively thin sheets, but also allow describing a very broad number of complex geometries. Their mathematical description favors a very efficient numerical treatment, in particular when used in the context of contact mechanics. Here, the contact between superellipsoids and nodal meshes, such as those used in finite elements, is analyzed. Based on the analytical properties of the implicit form of the superellipsoid equations, defined in a local coordinate frame, all the quantities necessary to handle a contact problem are derived. Recognizing that one of the most expensive tasks in contact mechanics is the contact detection, a three-stage contact search strategy is envisaged and implemented. Only in the close proximity between a node and the superellipsoid is a detailed contact search performed. In case of contact, the contact forces and their application points are evaluated using a continuous contact force model based on a penalty formulation. The existence of friction forces is considered. The methods developed and implemented for the contact between superellipsoids and nodal meshes are demonstrated and discussed with two contact scenarios comprising the impact of a superellipsoid on a hanging ‘towel’, and the contact of several superellipsoids with a flexible elastic platform.

超椭球体是超二次曲线族的一部分，具有几何和数学特性，不仅使它们适合于表示实体（从球体到相对薄的薄片），而且还可以描述非常广泛的复杂几何形状。它们的数学描述有利于非常有效的数值处理，尤其是在接触力学中使​​用时。在此，分析了超椭圆体和节点网格（例如有限元中使用的网格）之间的接触。根据在局部坐标系中定义的超椭球方程的隐式形式的解析性质，得出处理接触问题所需的所有量。认识到接触力学中最昂贵的任务之一是接触检测，设想并实施了三阶段联系人搜索策略。仅在节点和超椭球体之间非常接近时，才执行详细的联系人搜索。在接触的情况下，使用基于惩罚公式的连续接触力模型评估接触力及其作用点。考虑到摩擦力的存在。通过两种接触场景，论证和讨论了为超椭球体和节点网格之间的接触而开发和实施的方法，包括超椭球体对悬挂的“毛巾”的影响以及几种超椭球体与柔性弹性平台的接触。根据惩罚公式，使用连续接触力模型评估接触力及其作用点。考虑到摩擦力的存在。通过两种接触场景，论证和讨论了为超椭球体和节点网格之间的接触而开发和实施的方法，包括超椭球体对悬挂的“毛巾”的影响以及几种超椭球体与柔性弹性平台的接触。根据惩罚公式，使用连续接触力模型评估接触力及其作用点。考虑到摩擦力的存在。通过两种接触场景，论证和讨论了为超椭球体和节点网格之间的接触而开发和实施的方法，包括超椭球体对悬挂的“毛巾”的影响以及几种超椭球体与柔性弹性平台的接触。