Effect of the Order of the Finite Element and Selection of the Constrained Modesin Deformable Body Dynamics

摘要

Finite elements with different orders can be used in the analysis of constraineddeformable bodies that undergo large rigid body displacements. The constrained mode shapes resulting from the use of finite clements with different orders differ in the way the stiffness of the body bending and extension are defined. The constrained modes also depend on the selection of the boundary conditions. Using the same type of finite element, different sets of boundary conditions lead to different sets of constrained modes. In this investigation, the effect of the order of the element as well as the selection of the constrained mode shapes is examined numerically. To this end, the constant strain three node triangular element and the quadratic six node triangular element are used. The results obtained using the three node triangular element are compared with the higher order six node triangular element. The equations of motion for the three and six node triangular elements arc formulated from assumed linear and quadratic displacement fields, respectively. Both assumed displacement fields and describe large rigid body translational and rotational displacements. Consequently, the dynamic formulation presented in this investigation can also be used in the large deformation analysis. Using the finite element displacement field, the mass, stiffness, and inertia invariants of the three and six-node triangular elements arc formulated.