Tangent stiffness matrix

About: Tangent stiffness matrix is a research topic. Over the lifetime, 1031 publications have been published within this topic receiving 21140 citations.

Large Rotations in Structural Mechanics — Overview

Abstract: Some basic aspects on the handling of finite rotations in structural mechanics are presented in this overview.

A field consistency based co-rotational finite element procedure for 2d quadrilateral element

Abstract: Although there are a lot of research achivements for co-rotational procedure of a 2D quadrilateral element, most of these elements were based on geometric consisitency and produced a symmertric element tangential stiffness matrix.For elements of field consistency, there are less research works so far.Based on the field consistency principle of co-rotational procedure, a simple tangent stiffness matrix for the 2D quadrilateral element under large rotation with small strain is proposed in this paper.Comparied with the symmetric tangential stiffness matrix of geometric consistency, the element tangential stiffness matrix is asymmetric but less of computation.In nonlinear computation, this is positively meaningful as the round off errors accumulate with the increase of computation of element stiffness matriecs and consequently lead to the possibility of iteration disconvergence.In collaboration with the proposed asymmetric element stiffness matrix, an unified incremental iteration scheme of combining displacement increamental method and load increamental method is employed for the solution of resulting nonlinear FEM equations and following the procedure mentioned above and its corresponding formulation, a FORTRAN computer program, named NSAP, has been developed.Computations and analysis for plane beams and arches have verified the correctness of the element's formulation, the high efficency of the program and the strong nonlinear computation ability of the method.It is cable of analyzing nonlinear behavior of planar stress of beams and arches.Computations presented reflect preferably a comprehensive understanding of geometrical nonlinear characteristics of beams and arches, could be beneficial for the engineeing designers.

Static Stiffness Analysis and Simulation of 6-PTRT Parallel Robot

Abstract: To reveal the static stiffness behavior of a 6-PTRT parallel robot and find out its change rule in order to provide the reasonable parameters for the structural design, the stiffness characteristics of this parallel mechanism was studied. Based on the influence coefficient method, a static stiffness model for 6-PTRT parallel robot was established. The proposed model considered not only the axis stiffness of actuator but also the stiffness of passive joints, and the change of Jacobian matrix and first-order influence coefficient brought about by tiny change of the parallel robot mechanism's configuration under external wrench. The static stiffness matrix of parallel robot in initial position and its stiffness distribution rules for a certain workspace were given by numerical calculation and finite element method, which comparatively verify the exactness of stiffness model.

MATLAB-Based Calculation for Element Stiffness Matrix of Spatial Beam

Abstract: In order to solve the difficulties while computing the element stiffness matrix of spatial beam and to improve its computing efficiency, works were carried out by the capabilities symbolic and matrix operation of MATLAB. The element stiffness matrixes of spatial beam with shear effect considered or not were deduced and computed respectively, a part of source code for calculating these matrices were provided as well. Results show that MATLAB is very advantageous in the calculation of element stiffness matrix of space beam. It provides a new idea to compute the element stiffness matrix of spatial beam and other elements. Thus, it has a good theoretical and practical value in engineering.

Development of corotational formulated FEM for application to 30m class large deployable reflector

Abstract: JAXA, Japan Aerospace Exploration Agency, is now developing a corotational formulated finite element analysis method and its software Origami/ETS for the development of 30m class large deployable reflectors. For the reason that the deployable reflector is composed of beams, cables and mesh, this analysis method is generalized for finite elements with multiple nodes, which are commonly used in linear finite element analyses. The large displacement and rotation are taken into account by the corotational formulation. The tangent stiffness matrix for finite elements with multiple nodes is obtained as follows; the geometric stiffness matrix of two node elements is derived by taking variation of the element's corotational matrix from the virtual work of finite elements with large displacement; similarly the geometric stiffness matrix for three node elements is derived; as the extension of two and three node element theories, the geometric stiffness matrix for multiple node elements is derived; with the geometric stiffness matrix for multiple node elements, the tangent stiffness matrix is obtained. The analysis method is applied for the deployment analysis and static structural analysis of the 30m class large deployable reflector. In the deployment analysis, it is confirmed that this method stably analyzes the deployment motion from the deployment configuration to the stowed configuration of the reflector. In the static analysis, it is confirmed that the mesh structure is analyzed successfully. The 30m class large deployable reflector is now still being developed and is about to undergo several tests with its prototypes. This analysis method will be used in the tests and verifications of the reflector.