GEOMETRIC AND COMPUTER MODELING OF CURVED SURFACES OF MEMBRANE COVERS ON A RECTANGULAR PLAN

Abstract

The article offers an analytical description and computer models of three curved surfaces of the membrane covering on a rectangular plan, which include a surface model that is concave in one direction, in two directions, and convex-concave. All models are obtained based on the following conceptual sequence of actions: geometric scheme of the model – analytical description in BN-calculus – computer model of the desired surface. This approach allows you not only to get a computer model of the desired geometric object in the desired parameterization, but also to make the necessary adjustments at each stage of modeling. Geometrically, all the guide lines and forming lines of the modeled surfaces consist of simple geometric objects such as straight lines and circles. However, they were determined not only in the desired parameterization in this way, but also taking into account their mutual position, which determines the initial reference lines and the set value of the maximum deflection of the beam and membrane shells. The obtained analytical descriptions of geometric objects are combined into a computational algorithm implemented in the Maple software package. As a result, the visualized computer models of the obtained surfaces were exported to dxf format, taking into account the required density of rectangular finite elements for direct import into the system of finite element analysis of the stress-strain state of SCAD Office structures, followed by a computational experiment. Thus, all geometric information, taking into account the choice of the density of the finite element network, is provided by the proposed approach to modeling membrane covering shells under pre-set conditions, and the physical and mechanical properties of the material necessary for calculating the stress-strain state of structures are set directly in the computational system of finite element analysis in the modeling process.