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Free flexible element
Source publication
Equations of motion of a finite element in absolute coordinates including mass matrix, generalized inertia and internal forces are derived. A trapezoidal element for dynamic models of flexible shells in the shape of surface of revolution is considered. The element can be used for modeling dynamics of automotive tire and air spring bellows and some...
Contexts in source publication
Context 1
... idea for derivation of equations of motion of a flexible body in multibody system dynamics consists of splitting its spatial movement on a gross motion of a reference frame and small elastic deformations [7]. It is supposed that the flexible body is divided into a set of finite elements. Consider a finite element, which moves freely in 3D space, Fig. 1. Let us assume that n nodes are connected with the element. Positions of the node-fixed systems of coordinates SCi relative to the inertial frame of reference SCO are determined by the radius-vectors and the direct cosine (rotation) matrices . Hereafter in the paper, the abbreviation SC is used for the system of coordinate ...
Context 2
... where denotes a diagonal matrix. Consider the principle of virtual work for generation of equations of motion of the finite element [7], taking into account the work of inertia and elastic forces only (11) Here and a are the virtual displacement and acceleration of a point, respectively, whose position relative to SCF in Fig. 1 is determined by the vector r; dm and dV are the mass and volume of an infinitesimal part of the element; and are the elements of the stress and strain ...
Context 3
... position of an arbitrary point of the element relative to SCO according to Fig. 1 is (12) which gives the expressions for the virtual displacement and acceleration (13) Here and below, the ~ sign over the vector indicates a skew-symmetric matrix generated by the vector and used for the matrix notation of the vector product, for example (14) are the vectors of angular velocity, angular acceleration and the virtual ...
Similar publications
Citations
... In railway network, the numerical algorithms which are based on Kalker's approach [28,29] to calculate the normal and shear stress distribution in rail-wheel contact are widely used to study the mutual influence of contact conditions and rail-wheel dynamics, and also to analyze the damage and fracture processes in rails and wheels [30]. In [31,32] the program package "Universal Mechanism" is intended for simulation of kinematics and dynamics of planar and spatial mechanical systems, including the train motion (UM Loco). These studies have shown that the contact stresses which depend on the shapes of contacting bodies, the dynamic forces and the interface conditions (friction, surface roughness, adhesion, etc), influence essentially on service However, qualitative analysis of relatively simple coupled problems which is based on analytical or semi-analytical solutions of both contact mechanics and dynamics equations is of interest since it gives deep understanding of the mutual influence of the contact characteristics and dynamics effects. ...
This review presents a collection of the solved dynamic problems taking into account the normal and shear stress distributions in the contact region due to the deformation of contacting bodies. The considered dynamic problems differ in the number of degrees of freedom and the type of relative displacements of contacting bodies (2-D models with rolling and sliding, 3-D models with sliding and spinning, 3-D models with sliding, rolling and spinning). The contact mechanics solutions are used in formulation of the dynamic problems, which are studied based on the analytical or semi-analytical approach. The effects of the mechanical properties of the contacting bodies and the contact conditions on the dynamics are analyzed and discussed.
