The article discusses the problem of heating the wall in connection with the occurrence of a fire source. The conditions of convective heat exchange with the environment are considered on the wall surface. At a known ignition temperature of wood, the time it takes for the wall surface to reach this temperature is found. The problem is solved for a homogeneous wall made of a single material, as well as for an inhomogeneous wall in which a thin layer of wood is followed by a thick thermal insulation layer. The problem is solved analytically, as well as by the finite element method. The solution of the problem by the finite difference method is also considered.

Keywords: wood, thermal insulation layer, ignition temperature, convection, finite element method, finite difference method, thermal conductivity problem

In this paper we consider some problems of economics and organization of construction which can be solved by linear programming method. In the first problem it is required to determine the set of construction machines for excavation of given amount of soil to minimize the cost of work execution. In the second problem the earth is transported from two pits and it is required to determine how much earth must be digged from each of the two pits to provide for the minimum cost of transportation.

Keywords: soil excavation, sand, crushed stone, minimum cost, linear programming, two-phase simplex-method

In this article the results of analysis of special simply-supported plate by theory of plates of moderate thickness are presented. The special feature of this plate consists in specification of special boundary conditions on its edges which are different from usually specified boundary conditions. The uniformly distributed load is acting upon the plate. In this article the results of analysis by the finite element method are presented

Keywords: simply-supported plate, theory of thick plates, theory of plates of moderate thickness, Mindlin plate theory, Kirchhoff plate theory, bending moment, twisting moment, shear force, finite element method

In this paper we describe efficient Matlab-based implementation of the finite element solver for the problem of bending of Mindlin plates. This solver is tested on fine meshes consisting of a large number of linear rectangular finite elements. The performance of this solver is so good that even for fine meshes considered the CPU time is small enough.

Keywords: simply-supported plate, Mindlin plate theory, sparse solver, Matlab, finite element method