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.

Effects of tangent operators on prediction accuracy of meso-mechanical constitutive model of elasto-plastic composites

Abstract: With a newly developed homogenization cyclic constitutive model of particle reinforced metal matrix composites [Guo et al. (2011)], the effects of tangent operators, i.e., continuum and algorithmic tangent operators [defined by Doghri and Ouaar (2003)] on the accuracy of the developed meso-mechanical constitutive model to predict the monotonic tensile and uniaxial ratchetting deformations of SiCP/6061Al composites were investigated in this work. The predictions were obtained by the developed model with the choices of different tangent operators and various magnitudes of load increments. Comparison of prediction accuracy and necessary error analysis on the results obtained by different tangent operators were conducted. It is shown that: the stress or strain difference in each load increment and produced by using different tangent operators will accumulate step by step; accurate prediction should be obtained by employing a load increment small enough, especially when the algorithmic tangent operator is used in predicting the uniaxial ratchetting of the composites.

Numerical modeling of transient creep in

Abstract: Transient creep, an important deformation mechanism for polycrys- talline ice at quasi-static strain rates, is characterized by rate and temperature sensitivity, by isotropic and kinematic strain hardening, as well as by fabric and deformation-induced anisotropy. A physically based constitutive model, using in- ternal state variables, has been developed by Shyam Sunder and Wu (1989a, b) to describe the multiaxial behavior of ice undergoing transient creep. To solve bound- ary value problems using this constitutive theory requires the numerical time in- tegration of a coupled set of stiff and highly nonlinear first-order differential equa- tions. A closed-form Newton-Raphson (tangent) formulation, in conjunction with the a-method of integration, is developed to solve the constitutive equations. The fully consistent constitutive Jacobian matrix that is used to assemble the finite element tangent stiffness matrix is also established in closed form. This algorithm is implemented as a subroutine in the finite element program ABAQUS and its predictions are verified against experimental data and known solutions. The im- portance of transient creep is demonstrated by performing simulations of: (1) Ar- rested subsurface penetration; and (2) in-plane indentation of a floating ice sheet.

Alternative first principle approach for determination of elements of beam stiffness matrix

Abstract: Stiffness coefficients which in essence are elements of stiffness matrix of a uniform beam element are derived in this work from first principles using elastic curve equation and initial value method. The obtained initial value solution enables exact values of stiffness coefficients, fixed end moments and shears as well as displacement (deflection and rotation) of any given beam element under arbitrary lateral load to be evaluated.

Linearized Dynamic Analysis of Weightless Sagging Planar Elastic Cables

Abstract: Nonlinear dynamic analysis of elastic structures is known to be much more complex than their linear analysis. There are many sources of nonlinearity of the structural response of elastic cables, viz., physical nonlinearity due to nonlinear tension–extension relations, geometric nonlinearity associated with finite elastic displacements and nonlinearity of nodal load–displacement relations due to the presence of self-weight. Incremental second-order differential equations of motion are used to predict the vibration amplitudes relative to the equilibrium state caused by additional dynamic forces. Generally, the tangent stiffness matrices are determined by adding the tangent elastic and geometric stiffness matrices. Many a time, an approximate linearized dynamic analysis is attempted. In this paper, the initial tangent stiffness matrix corresponding to the equilibrium state is used in the second-order linear differential equation of motion. The dynamic response relative to the equilibrium state of the structure subjected to additional dynamic loads is predicted. The predictions of linearized dynamic analysis are generally considered acceptable for small elastic displacements from the equilibrium state. The validity of such linearized dynamic analysis for elasto-flexible cables obeying third-order differential equation of motion is explored.

Exact elastic stability analysis based on dynamic stiffness method

Abstract: The article is dedicated to the discussion on the exact dynamic stiffness matrix method applied to the problems of elastic stability of engineering structures. The detailed formulation of the member dynamic stiffness matrix for beams is presented along with the general guidelines on automatisation of the assembly of member dynamic stiffness matrices into the global matrix that corresponds to the whole structure. The advantage of the dynamic stiffness matrix in case of parametric studies is explained. The problem of computing the eigenvalues of transcendental matrix is addressed. The straightforward approach as well as a powerful Witrick-Williams algorithm are discussed in details. The general guidelines on programming the DS matrix method are given as well.