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.

Nonlinear analysis of steel tube initial stress effect in stell tube on bearing capacity for CFST arch bridges

Abstract: Based on equilibrium equation of nonlinear problem and nonlinear geometric equation of spatial beam element,explicit formula of tangent stiffness matrix for spatial beam element was deduced,its constitutive relationship includes the initial stress and initial strain.According to structure character of dumbbell section,a combined spatial beam element is presented for computing and storing steel tube initial stress.Method of element division was described about bearing capacity analysis for concrete filled steel tubular(CFST) arch bridge.A special program was developed.The results calculated by program were in accordance with tests.A lot of bearing capacity calculation are performed,with regard to different coefficients of initial stress steel tube,different sectional steel ratios and different spans.Results show that initial stress of steel tube could reduce the capacity of CFST arch bridge,the reduction extent depends on the sectional type of arch rib,and the maximum reduction can exceed 30%.Finally,practical formulas of bearing capacity influence factor are given for the CFST arch bridge with three common sectional types.

Direct Stiffness Method

Abstract: High Quality Content by WIKIPEDIA articles! As one of the methods of structural analysis, the direct stiffness method (DSM), also known as the displacement method or matrix stiffness method, is particularly suited for computer-automated analysis of complex structures including the statically indeterminate type. It is a matrix method that makes use of the members' stiffness relations for computing member forces and displacements in structures. The direct stiffness method is the most common implementation of the finite element method (FEM). In applying the method, the system must be modeled as a set of simpler, idealized elements interconnected at the nodes. The material stiffness properties of these elements are then, through matrix mathematics, compiled into a single matrix equation which governs the behaviour of the entire idealized structure. The structure's unknown displacements and forces can then be determined by solving this equation. The direct stiffness method forms the basis for most commercial and free source finite element software. The direct stiffness method originated in the field of aerospace.

Nonlinear Truss Analysis by One Matrix Inversion

Abstract: A new method for nonlinear structural analysis has been developed. The novelty of the method is that only one stiffness matrix inversion is required without the need for updating and reinverting the matrix at every load increment. This stiffness matrix is not necessarily the real stiffness matrix of the structure. Instead any stiffness matrix compatible with the geometry and the constraints of the truss can be used. The advantage of this option is that if the design of some members is revised the already inverted and stored matrix is used for the analysis of the revised structure. Nonlinearities due to strain hardening, strain softening, buckling, breaking, and stiffness degradation are handled by iterations involving only multiplications of the banded matrix with a transformed force vector. The inversion of the half-banded original stiffness matrix is done using Gauss elimination performed on the half-banded matrix without destroying the bandedness, and the inverted matrix replaces the original without the need for additional storage. The coefficients for the transformation of the force vector are stored permanently in a new matrix of size equal to the size of the half-banded original. Thus, the total storage needed is equal to the storage for the banded original stiffness. Because, after the Gauss elimination, only multiplications of a matrix with a vector are involved, the method is computationally efficient. The method is not a step-by-step procedure. Any load increment can be applied, therefore, proportional, nonproportional, and cyclic loads are treated in a unified way. The energy dissipation and the residual stresses and strains after one or more cycles are readily available, and thus the method can be used in quasi-dynamic analysis (e.g. pushover) for an evaluation of the dynamic parameters of the structure.

Efficient dynamic formulation for co-rotational 2D beams

Abstract: 2D beam element, Corotational method, Nonlinear dynamic analysis, Dynamics, Interpolation, Matrix algebra, Nonlinear analysis, Stiffness matrix, Structural dynamics, Beam elements, Co-rotational fo ...