A FINITE-ELEMENT METHODOLOGY OF ANALYZING A 3D PROBLEM OF DYNAMICS OF STRUCTURES STIFFENED BY A SYSTEM OF REINFORCING RODS

Abstract

Nonstationary deformation of spatial structures made of piecewise-homogeneous isotropic materials (matrices), stiffened by a discrete system of curvilinear rods sustaining effects of tension-compression, is considered. It is assumed that the number of reinforcing rods is not large and their arrangement in the main material can be irregular. In analyzing such structures, the averaging methods used in mechanics of composite materials may become inapplicable. The defining equation set is formulated in Lagrange variables. Equations of motion are derived from the virtual work power balance. Kinematic relations are defined in the metrics of a current state. Relations of Beton's yield theory are used as equations of state for metals and alloys, and masonry is considered as a hetero-modular medium, the equations of state of which depend on the type of stressed-strained state and damage degree. The problem is analyzed using a momentary scheme of the finite element method and a cross-type explicit finite-difference time integration scheme. The analyzed region is discretized using 8-node finite elements with a poly-linear approximation of displacement velocities. The curvilinear, in a general case, reinforcing rods are discretized into straight sections, the spatial location of which is defined by the coordinates of the points of their intersection with the sides of the finite elements of the mesh of the main material. Slipping between the reinforcement and the binding material is not considered. Stresses in the rod are substituted for by statically equivalent forces of the nodes of the finite element of the matrix, which are projected onto a common coordinate system and summed with node forces from stresses in the main material and external loading. To verify the developed finite-element methodology, a number of benchmark problems have been analyzed.