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 Single-Layer Reticulated Spherical Shells Under Static and Dynamic Loads

Abstract: A nonlinear finite element technique is developed for analyzing the nonlinear static and dynamic responses as well as the nonlinear stability of single-layer reticulated shells under external loads, in which the nonlinear three-dimensional beam elements are employed. Using the updated Lagrangian formulation, we derive a tangent stiffness matrix of three-dimensional beam element, considering the geometric nonlinearity of the element. Moreover, the modified Newton-Raphson method is employed for the solution of the nonlinear equilibrium equations, and the Newmark-β method is adopted for determining the seismic response of single-layer reticulated shells. An improved arc-length method, in which the current stiffness parameter is used to reflect the nonlinear degree of such space structures, is presented for determining the load increment for the structural stability analysis. In addition, an accurate incremental method is developed for computing the large rotations of the space structures. The developed appro...

Second-order lower radial tangent derivatives and applications to set-valued optimization.

Abstract: We introduce the concepts of second-order radial composed tangent derivative, second-order radial tangent derivative, second-order lower radial composed tangent derivative, and second-order lower radial tangent derivative for set-valued maps by means of a radial tangent cone, second-order radial tangent set, lower radial tangent cone, and second-order lower radial tangent set, respectively. Some properties of second-order tangent derivatives are discussed, using which second-order necessary optimality conditions are established for a point pair to be a Henig efficient element of a set-valued optimization problem, and in the expressions the second-order tangent derivatives of the objective function and the constraint function are separated.

Inelastic Buckling Analysis of Frames with Semi-Rigid Joints

Abstract: An improved method for evaluating effective buckling length of semi-rigid frame with inelastic behavior is newly proposed. Also, generalized exact tangential stiffness matrix with rotationally semi-rigid connections is adopted in previous studies. Therefore, the system buckling load of structure with inelastic behaviors can be exactly obtained by only one element per one straight member for inelastic problems. And the linearized elastic stiffness matrix and the geometric stiffness matrix of semi-rigid frame are utilized by taking into account 4th terms of taylor series from the exact tangent stiffness matrix. On the other hands, two inelastic analysis programs(M1, M2) are newly formulated. Where, M1 based on exact tangent stiffness matrix is programmed by iterative determinant search method and M2 is using linear algorithm with elastic and geometric matrices. Finally, in order to verify this present theory, various numerical examples are introduced and the effective buckling length of semi-rigid frames with inelastic materials are investigated.

Static and dynamic non-linear analysis of structures

Abstract: The paper discusses some recent advances in the non-linear finite element method for the analysis of structures. In particular, the paper concentrates on beams and shells. It starts with statics and describes a new co-rotational formulation which relies on a matrix defining the relationship between the pseudo-vector associated with the spin of the local element frame and the changes in the global displacement variables. It is shown that certain terms can be neglected in the derivation of the tangent stiffness matrix. The paper moves on to consider implicit non-linear dynamics and describes various energy conserving or approximately energy conserving techniques. It shows, that in contrast to the widely used trapezoidal Newmark method (and also the α method), these techniques are very stable in the non-linear regime. The dynamic solution procedures are used in conjunction with a set of non-linear master-slave relationships which allow the modelling of joints. Using these various techniques, the finite element method becomes an attractive tool for the analysis of flexible rotating mechanical systems.