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.

Spatial stiffness realization with parallel springs using geometric parameters

Abstract: This paper investigates the synthesis of a spatial stiffness matrix using simple line springs. A new algorithm is developed, which enables the selection of constituent springs based on their positions and directions. The constraining space of the line springs is then investigated. It is shown that an isotropic stiffness matrix, in general, can be split into the sum of two rank-3 stiffness matrices. The three line springs of the first matrix can be selected to pass through any arbitrary points in space, while the three line springs of the second stiffness matrix lie on a quadric surface, which is usually a hyperboloid of one sheet.

A formulation for the 4‐node quadrilateral element

Abstract: A formulation for the plane 4-node quadrilateral finite element is developed based on the principle of virtual displacements for a deformable body. Incompatible modes are added to the standard displacement field. Then expressions for gradient operators are obtained from an expansion of the basis functions into a second-order Taylor series in the physical co-ordinates. The internal degrees of freedom of the incompatible modes are eliminated on the element level. A modified change of variables is used to integrate the element matrices. For a linear elastic material, the element stiffness matrix can be separated into two parts. These are equivalent to a stiffness matrix obtained from underintegration and a stabilization matrix. The formulation includes the cases of plane stress and plane strain as well as the analysis of incompressible materials. Further, the approach is suitable for non-linear analysis. There, an application is given for the calculation of inelastic problems in physically non-linear elasticity. The element is efficient to implement and it is frame invariant. Locking effects and zero-energy modes are avoided as well as singularities of the stiffness matrix due to geometric distortion. A high accuracy is obtained for numerical solutions in displacements and stresses.

Comparison between sparse stiffness matrix and sub‐structure methods

Abstract: Recent publications have emphasized the advantages of the sparseness of the over-all stiffness matrix of a structure. An alternative to setting up the over-all stiffness matrix is to use sub-structures. The main purpose of this paper is to show that there is equivalence between these two approaches when rows are not interchanged. It follows that a sparse matrix method can never be more efficient than the sub-structure method, if a suitable choice of sub-structures is assumed. However when identical sub-structures are contained within a structure the repetition can be utilized by the sub-structure method. In such cases the sub-structure method will often be quicker than the best sparse matrix solution.

BEM analysis of laterally loaded pile groups in multi-layered transversely isotropic soils

Abstract: Based on an analytical layer-element solution of multi-layered transversely isotropic soils, a boundary element method is adopted to analyze laterally loaded fixed-head pile groups. The pile–soil–pile interaction is considered directly by coupling the global stiffness matrix of pile groups and the soil׳s global flexibility matrix at the pile–soil interface. Good and reasonable agreement is obtained between the proposed and published solutions. A typical numerical example is presented to study the behavior of laterally loaded pile groups embedded in multi-layered transversely isotropic soils.