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.

Analysis of dynamic characteristics of structural joints using stiffness influence coefficients

Abstract: This paper proposes a new modeling method for joints in mechanical structures in order to reduce the errors in eigenvalue analysis due to joint modeling. The new modeling method uses both a stiffness influence method and a condensation method to obtain the dynamic characteristic matrix of the joint region. It also employs the displacement and reaction of finely modeled finite element analysis in the calculation of stiffness influence coefficients. In order to check the validity of the proposed method, natural frequencies and mode shapes of a simple structure with a bolted joint are investigated by the proposed method and by experiments. The eigenvalue analysis using the proposed method shows more accurate results than that using rigid joints modeling, when the natural frequencies are compared with the experimental results. In addition, the differences between the natural frequencies obtained by the proposed method and those by the rigid joints modeling are notable in the modes where the joint has elastic deformation.

Fast MATLAB assembly of FEM matrices in 2D and 3D using cell-array approach

Abstract: We propose a MATLAB implementation of the P1 finite element method for the numerical solutions of the Poisson problem and the linear elasticity problem in two-dimensional (2D) and three-dimensional (3D). The code consists of vectorized (and short) assembling functions for the matrices (mass and stiffness) and the right-hand sides. Since for the P1 finite element, the element mass matrix and right-hand side are simple, the implementation uses only the MATLAB function sparse on the elements volume. For the stiffness matrix, to obtain a MATLAB implementation close to the standard form, cell-arrays are used to store the gradients of the element basis functions. The assembling procedure can then use matrix/vector products on small size cell-arrays. Numerical experiments show that our implementation is fast, scalable with respect to time, and outperforms existing vectorized MATLAB FEM codes.

Alternate hybrid stress finite element models

Abstract: Alternate hybrid stress finite element models in which the internal equilibrium equations are satisfied on the average only, while the equilibrium equations along the interelement boundaries and the static boundary conditions are adhered to exactly a priori, are developed. The variational principle and the corresponding finite element formulation, which allows the standard direct stiffness method of structural analysis to be used, are discussed. Triangular elements for a moderately thick plate and a doubly-curved shallow thin shell are developed. Kinematic displacement modes, convergence criteria and bounds for the direct flexibility-influence coefficient are examined.

Fluid finite elements for added mass calculations

Abstract: The equations for the free undamped vibration of a structure in an ideal incompressible fluid medium and their finite element formulation are briefly reviewed. The relevant matrices (stiffness and loading) for two prismatic fluid elements are given explicitly and some numerical results are presented.