Frequency Domain Spectral Element Model for the Vibration Analysis of a Thin Plate with Arbitrary Boundary Conditions

We propose a new spectral element model for finite rectangular plate elements with arbitrary boundary conditions. The new spectral element model is developed by modifying the boundary splitting method used in our previous study so that the four corner nodes of a finite rectangular plate element become active. Thus, the new spectral element model can be applied to any finite rectangular plate element with arbitrary boundary conditions, while the spectral element model introduced in the our previous study is valid only for finite rectangular plate elements with four fixed corner nodes. The new spectral element model can be used as a generic finite element model because it can be assembled in any plate direction. The accuracy and computational efficiency of the new spectral element model are validated by a comparison with exact solutions, solutions obtained by the standard finite element method, and solutions from the commercial finite element analysis package ANSYS.

Three-Dimensional Fully Parameterized Triangular Plate Element Based on the Absolute Nodal Coordinate Formulation

In this work, a new three-dimensional fully parameterized triangular plate element based on the absolute nodal coordinate formulation (ANCF) is introduced. This plate element has 12 coordinates per node; therefore, it can be used in thick plate applications. The proposed 12 shape functions are obtained by adding three shape functions to the nine shape functions that were previously used with the ANCF thin triangular plate element. Unlike the existing ANCF thin triangular plate element, which allows only the use of classical Kirchoff's plate theory, the fully parameterized ANCF triangular plate element proposed in this work allows for the use of a general continuum mechanics approach and also allows for a straight forward implementation of general nonlinear constitutive equations. Moreover, all deformation modes including thickness deformation can be captured using the fully parameterized ANCF triangular plate element proposed in this paper. The numerical results obtained in this investigation show that in case of negligible deformation, the fully parameterized ANCF triangular plate element behaves like a rigid body. Moreover, it is found that there is a good agreement between the solutions obtained using the proposed fully parameterized ANCF triangular plate element and the theoretical model in the case of small deformations. Furthermore, it is shown that the results of the proposed element agree well with the results obtained using the existing fully parameterized ANCF rectangular plate element when large deformation conditions are applied. The twist behavior of the proposed element is verified by comparison with the results obtained using a conventional nonlinear rectangular plate element.

Mean-Axis Conditions for Finite Elements Undergoing Large Rotations and Translations

The mean-axis conditions for three types of finite elements that undergo large rotation and translation are derived. The cases include two Lagrangian planar elements (linear triangle and linear rectangle) and a three dimensional rectangular plate element. Each case includes two elements connected at the nodes. Three separate coordinate systems are used in describing the systems. The numerical values of different matrices including the mass matrix are presented for specific cases. It may be seen that the non-linear mass matrix is expressed in terms of a set of time-invariand matrices. The total mass matrix of the body i is obtained by assembling the individual mass matrices of the finite elements of body i.