International Journal for Computational Civil and Structural Engineering

ISSN for PRINT: 1524-5845

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2005, Volume1

Pavel A. Akimov
Assistant Professor, Department of Applied Mathematics and Information Technology, Moscow State University of Civil Engineering, 26, Yaroslavskoe Shosse, 129337 Moscow, Russia

Alexander B. Zolotov, Professor
Department of Applied Mathematics and Information Technology, Moscow State University of Civil Engineering, 26, Yaroslavskoe Shosse, 129337, Moscow, Russia

This paper consists of four sections and is devoted to the discrete-continual variation-difference method (DCVDM) for two-dimensional and three-dimensional problems of structural analysis. Operational and variational formulations with the use of distribution are presented in the first chapter. The second one is dedicated to general principles of mesh approximation for boundary problems. In particular we studied questions dealing with approximation of domain, approximation of functions and approximations of operators. Mesh functions are introduced as well as corresponding mesh operations and various types of implementation. The results are rather efficient algorithms in respect to number of operations, computing time and required memory. Being a foreground subject, DCVDM is considered in the third section. The discrete-continual design model for structures with constant physical and geometrical parameters in one direction is offered on the basis of so-called discrete-continual mesh elements. Element coordinate systems, approximation of nodal unknowns, and construction of element nodal load vector are under consideration. Resolving multipoint boundary problems for systems of ordinary differential equations are given. Section 4 contains brief information about computer realization of DCVDM for structural analysis and corresponding software.

DOI: 10.1615/IntJCompCivStructEng.v1.i2.10 Download article, 1-20 pages

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