A dynamic finite element modeling technique for two-dimensional structures

The standard finite element method is used to analyze complex structures that require the solution of unsolvable partial differential equations. The solution for this method is based solely on static constraint modes(SCM's),and consider only linear displacement at the boundaries of the elements. Thus, a large number of degrees of freedom are needed for a dynamic analysis.The purpose of this research is to develop a modeling technique,to reduce the number of degrees of freedom,needed to obtain an exact solution for the dynamic analysis of two-dimensional structures. To do so,it is necessary to account for the additional motion neglected by the standard finite element method. The dynamic finite element method accounts for this additional motion with the inclusion of interface restrained assumed modes(IRAM's),and frequencies in the mass and stiffness matrices.Fortran programs and subroutines have been written for the dynamic analysis of the triangular and quadrilateral elements.It is noted that the number of interface restrained assumed modes(IRAM's)needed to obtain a desired number of converged frequencies,is dependent on element size,model stiffness,and the desired percentage error.The dynamic finite element method offers an average savings of44%,for less than1%error,an average savings of54%for less than 3%error, and an average savings of62%for less than5%error,when the triangular element is used for the finite elementmodel.VThe dynamic finite element method offers an average savings of27%, for the 24-Node quadrilateral element,and an average savings of11%for the 16-Node quadrilateral element for less than 1%error.The dynamic finite element method has consistently used fewer degrees of freedom,than the standard finite element method,to obtain a desired number of converged frequencies. The Inclusion of interface restrained assumed modes(IRAM's) and corresponding frequencies,provide an accurate model,and thus motefirequenciesconverge.