Analytical matrix solutions of linear ordinary differential equations with constant coefficients

Abstract

Abstract The article puts forward a modified finite element method based on decomposition and analytical solution techniques. The algorithm is as follows. A complex structure is divided into simple form sub-regions which involve partial differential equations. Next, the equations are decomposed. The decomposed equation solutions are written using analytical solution formulae. Meanwhile, the finite element size of the method proposed is defined only by the value of an averaging interval of required functions, since ordinary differential equation formulae are analytical. The algorithm has been tested by solving rectangular plate and bicurved shallow shell bending problems. The results proved proper convergence to precise values with increasing number of finite elements.