全体座標系と要素座標系を併用したANCF板要素の定式化

抄録

This paper describes a development of the shear deformable plate element based on the absolute nodal coordinate formulation (ANCF) by using algebraic constraints. In the ANCF, there are two different approaches on the definition of the elastic forces within the finite element. The first method is a so-called continuum mechanics approach. In the other approach, a local element coordinate system is employed for the description of the element deformation. Latter approach suffers from highly nonlinear terms in expression for elastic forces depending on coordinate transformation. It is reported the calculation time is significantly decreased by introducing the constraints. This approach allows for the use of the global coordinate system and the element coordinate system at the same time. Therefore the description of the elastic force can be simpler form without coordinate transformation. This paper formulates the shear deformable plate elements by using the constraints. The locking problem due to highly order polynomials in the thickness direction is resolved by the description of the displacement field with the mid-surface and the fiber rotation. Moreover, the linear strain model is introduced to the description of the elastic force. Then, the result calculated by the derived equation is compared with the previous research.