Estruturas tridimensionais com propriedades mecânicas dos materiais representadas matematicamente por séries - aplicação à análise de pontes

Abstract

In this dissertation it is presented a numerical analysis of tridimensional structures, using the semi-analytical finite element process. The analysis is focused on simple supported, curved, skew or retangular bridges with arbitrary cross section. The analysis allows the consideration of diaphragms. The mechanical properties are expanded into FOURIER series, allowing for variations in the material and geometric characteristics of the structure. Besides the mechanical properties, all the other dependent variables are also expanded into FOURIER series. As a consequence of the series expansion of the mechanical properties, the system of equations becomes fully coupled and must be solved simultaneously. By grouping all FOURIER coefficients together at each nodal point the structural stiffness matrix, that results from the coupling between the harmonics, can be banded. The solution of the system of linear equations is obtained by the Gaussian elimination method, employing a block solver. A computer program is presented and applied to some examples.