Geometriškai netiesinio lenkiamo strypo baigtinio elemento standumo rodiklių nustatymas

Abstract

Two-dimensional geometrically non-linear beam element is considered in this paper. The explicit expressions of stiffness characteristics of element with three nodes are derived and tested. Among models of the geometrically non-linear beams, the elements with 2 nodes dominate [1-8]. Such elements produce constant axial force. The idea of more complex elements with tree nodes was suggested in [3]. In this paper geometrically non-linear flat bending beam element with 3 nodes for evaluating of axial force is investigated and nonlinear stiffness characteristics are derived. Basic relations of element e are derived using virtual displacement method. On the level of element e, the principle of virtual displacements is expressed by equalities (1-3). Using displacement approach, displacement functions are prescribed in the bounds of one finite element. Generalised deformations are obtained by introducing displacements approximation (4) and inserting them into non-linear geometric equations (5-6). Variation of deformation energy (3) is expressed in (7). Putting equality (7) into (1), it is possible to write equality of virtual works in terms of non-linear algebraic equations (8). Non-linear stiffness matrix is presented as the sum of 3 matrices (9). The first matrix [K0e,] (linear matrix) is the matrix of small deflections, which is independent on deformed shape. The second matrix [KNe] is the matrix of large deflections. The third matrix [КGe] is a geometrical stiffness matrix. It reflects the second member of equality (7). Expressions of geometrically non-linear stiffness matrices are greatly dependent on the introduced assumptions and appropriate elements. [...]