Direct stiffness method

About: Direct stiffness method is a research topic. Over the lifetime, 2584 publications have been published within this topic receiving 53131 citations.

Semi-implicit transient analysis procedures for structural dynamics analysis

Abstract: A semi-implicit direct time integration procedure is presented which avoids factorization of the implicit difference solution matrix. The procedure, if properly implemented, requires only vectorial calculations and hence needs the same computer core space as explicit integration procedures. Guidelines for splitting the stiffness matrix into upper and lower matrices are established, which among other things are designed to satisfy a correct transmission of rigid-body motions from element (or grid) to its adjacent elements.

Formulation of consistent restoring stiffness in ship hydroelastic analysis

Abstract: In this article, the role of the restoring stiffness, as one of the basic parameters in ship hydroelastic analysis, is brought out. It is formulated using the variational principle and the method of virtual displacements. It is shown that asymmetry of the restoring stiffness is a physical reality. Moreover, it is confirmed that modal variation, still disputed in the relevant literature, has to be taken into account to satisfy the ship’s stability. Consistent stiffness is formulated here by regarding stiffness definition as relation between forces and displacements. Hybrid stiffness known from the literature is wrong since some terms are specified as relation between forces and displacement gradient. Influence of the consistent and symmetrized stiffness matrix, and the hybrid one, on dynamic response is illustrated for a prismatic pontoon and a large container ship. It is found that the latter two matrices do not assure convergence of transfer functions of sectional forces to zero value as the wave frequency approaches zero. The rigid body and elastic responses are compared, and pertinent conclusions are drawn. It is also shown that it is not necessary to use the unified geometric and restoring stiffness for ordinary hydroelastic analysis of ship structures. The consistent formulation of the restoring stiffness matrix will be useful for extending linear potential theory hydrodynamic codes for rigid body analysis to deformable bodies.

Computer Analysis of large Linear Frames

Abstract: A procedure for static analysis of linear frames is described which deals exclusively with nonzero submatrices of the structure's stiffness matrix, thus virtually eliminating trivial arithmetic. The bookkeeping operations involved in the procedure require only a small amount of computer execution time; accordingly, low computer costs are obtained. The procedure involves no restrictions on stiffness matrix band width, as band matrix methods are not used. Frame and finite-element programs based on this procedure are applicable to structures having many thousands of degrees-of-freedom. Detailed execution cost data are given.