Discrete-continual Finite Element Method of Analysis for Three-dimensional Curvilinear Structures
This paper is devoted to discrete-continual finite element method (DCFEM) of analysis for three-dimensional curvilinear structures. Operational and variational formulations of the problem in the ring coordinate system are presented. The discrete-continual design model for structures with constant physical and geometrical parameters in longitudinal direction is offered on the basis of so-called curvilinear discrete-continual finite elements. Element coordinate system, approximation of nodal unknowns, construction of element nodal load vector are under consideration. Element system of differential equations is formulated with use of special generalized block-structured stiffness matrix of discrete-continual finite element. Local differential relations are formulated. Resultant multipoint boundary problem for system of ordinary differential equations is given. Method of analytical solution of multipoint boundary problems in structural analysis is offered as well. Its major peculiarities include universality, computer-oriented algorithm involving theory of distributions, computational stability, optimal conditionality of resultant systems, partial Jordan decomposition of matrix of coefficients, eliminating necessity of calculation of root vectors. Brief information concerning developed software is provided.