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Dimensionally reduced nonlinear solids with general loads and constitutive laws: theory and finite element formulation for rod-like bodies
International Journal of Solids and Structures ( IF 3.6 ) Pub Date : 2021-02-01 , DOI: 10.1016/j.ijsolstr.2020.11.024
Rafael Cantón-Sánchez , Ignacio Romero

Abstract Dimensionally reduced solids are formulated by linking the kinematics of a slender, rod-like body and a true, geometrically exact, rod. This link is enforced in such a way that the solid, where volumetric and surface loads can be applied, becomes slave of the rod, where the mechanical equilibrium is enforced. The model poses no limitations on the size of the deformations and displacements in either body and it can be used for quasistatic or dynamic analyses. A general finite-element approximation of the ensemble is described in detail, and shown to require only modifications at the assembly level for its implementation, resulting in large computational savings. These dimensionally reduced models are especially useful for problems such as fluid/solid interaction and contact where the surface forces among neighboring bodies need to be calculated accurately. By accounting for the internal energy in the slave solid instead of the rod, the proposed formulation allows also to model — without any additional ingredients — the mechanics of rods with complex material constitutive laws. Numerical examples illustrate the use of the new models in situations with complex loading and constitutive behavior.

中文翻译:

具有一般载荷和本构定律的降维非线性实体:杆状体的理论和有限元公式

摘要 尺寸缩减的固体是通过将细长的棒状体和真实的、几何精确的棒的运动学联系起来而制定的。这种链接以这样一种方式被强制执行,即可以施加体积和表面载荷的固体成为杆的从属,在那里强制实现机械平衡。该模型对任一物体的变形和位移大小没有限制,可用于准静态或动态分析。详细描述了整体的一般有限元近似,并表明只需要在装配级别进行修改即可实现,从而节省了大量的计算量。这些尺寸减少的模型对于需要准确计算相邻物体之间的表面力的流体/固体相互作用和接触等问题特别有用。通过考虑从属固体而不是棒中的内能,所提出的公式还允许对具有复杂材料本构定律的棒的力学进行建模——无需任何额外成分。数值例子说明了新模型在具有复杂载荷和本构行为的情况下的使用。
更新日期:2021-02-01
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