剛体要素を用いた有限要素法

概要

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A new finite element method was proposed to obtain the deformation of an elastic body in which several rigid bodies are involved. The procedures are as follows. 1) Divide only the elastic body into several elements, while each rigid body is treated as a rigid element. The displacement of the rigid element can be expressed by translational motions u, v and the rotation θ. 2) Represent the strain energy stored in the elastic element by a stiffness matrix and a nodal displacement vector. If one or more nodes of the element are coupled to a rigid element, the stiffness matrix is reconstructed by using (u, v, θ). 3) Assemble the elementwise stiffness matrix into a system matrix. To restrict the band width of the matrix, a method of arranging the system nodal displacement vector was also devised herein. The proposed method was applied to a simple model of a cantilever beam in which two rigid bodies are embedded. The results show the effectiveness of the method compared with the conventional FEM. For one of biomechanical applications, a lumbar spine model was treated by considering individual centrum as a rigid body and intervertebral discs as elastic bodies.
日本シミュレーション学会の論文
1988-06-15