Translational joint in a Finite Element Analysis program of 2D frames with straight and curved elements

Resumo

This paper describes the development of an algorithm for the structural analysis of bidimensional frames with straight and curved elements that include a translational joint which can be set to any specified angle. The code was written in Fortran following a Finite Element Method-based structure. Three elements were considered: a circumferential arc-shaped; a straight bar with cross-sectional height varying according to a linear polynomial function; and the traditional straight element with constant inertia. All Stiffness matrices and load vectors were derived from the inversion of their corresponding Flexibility matrices obtained using the Force Method. In a few cases, a Gaussian Quadrature was needed in order to calculate the integral. The resulting program was validated against solutions found in the scientific literature in addition to structures created and solved by the authors using the Virtual Work Method, and it is shown to give very accurate predictions for displacements and rotations as well as reactions and internal forces (axial, shear and bending).