Narrow Results

It is well-known that the domains of static stability and dynamic stability (even for a linear approach) do not match each other when the system is no more conservative and the dynamic approach is usually privileged, meaning that the dynamic stability domain is included in the static one. Following previous works proposing a new criterion of static stability of nonconservative systems and prolonging a paper of Gallina devoted to linear dynamic instability (flutter), we show in this paper some remarkable relations between the two approaches: contrary to the common thought, the new static stability criterion implies partially the dynamic one.

A comparative study is performed for the direct and iterative methods for updating the structural matrices based on measured data. The former was derived from the orthogonality constraints by replacing the modal vector of concern by the modal matrix in computing the correction matrices. ¹ The iterative method used is the improved inverse eigensenstivity method. ² Through the numerical studies, it was demonstrated that both methods yield good results. However, the direct updating method is found to be more suitable for engineering applications due to its ease in treating multi-modes and higher efficiency, especially for complicated structures.

This article presents the differential equation in the global coordinates governing the structural behavior of 3D curved beams existing in building structures and civil works. This differential equation presented is of the lower-triangular form, which allows us to obtain the transfer matrix, also of lower-triangular form and with unit diagonal, through simple integrals. The stiffness matrix is determined from the transfer matrix expression, only by reordering operations, without employing additional structural methods, energy theorems or other. This rearrangement can be more easily done under the global system, compared with the natural reference system, since the order of the matrices involved has been reduced. The examples presented show the process to apply this general procedure to derivation of the stiffness matrix of a member from its transfer expression, through reordering operations.

Presented herein is a matrix method for buckling analysis of general frames based on the Hencky bar-chain model comprising of rigid segments connected by hinges with elastic rotational springs. Unlike the conventional matrix method of structural analysis based on the Euler–Bernoulli beam theory, the Hencky bar-chain model (HBM) matrix method allows one to readily handle the localized changes in end restraint conditions or localized structural changes (such as local damage or local stiffening) by simply tweaking the spring stiffnesses. The developed HBM matrix method was applied to solve some illustrative example problems to demonstrate its versatility in solving the buckling problem of beams and frames with various boundary conditions and local changes. It is hoped that this easy-to-code HBM matrix method will be useful to engineers in solving frame buckling problems.

The objective of the present study is to investigate the stiffness of the knee joint, in order to provide a basis for developing a biofidelic pedestrian legform impactor. A biofidelic lower limb model was employed to replicate structural responses of the human knee joint by finite element simulations. In the simulation, a single displacement was imposed on the thigh or leg, and constrained six freedoms of the other part. As a result, nonlinear load-displacement data were approximated by a linear regression to determine the stiffness. Considering knee joint kinematics under lateral car-pedestrian impacts, a stiffness matrix was established including lateral bending, lateral shearing and torsion effects that significantly influence pedestrian lower limb injuries. Then, this stiffness matrix was applied in a developed legform model. The structural responses of the legform were obtained by the impact with a family car model. Finally, the legform biofidelity was evaluated by comparing the global kinematics of the pedestrian lower limb.

We propose a MATLAB implementation of the $P^1$ 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 $P^1$ 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.

An element edge method is developed for the evaluation of stiffness matrix for the 8-node brick element. Handling of large data leads to take more computational time in finite element analysis. The new set of quadrature consist of 13 sampling points and weights out which 12 points are at the edges of the brick element and one point is considered at the center of the element. The new set of sampling points is a mimic of Gauss numerical integration method. Finally, the proposed element edge method is evaluated using the standard benchmarked problems and compared the results with conventional Gauss integration method and found that CPU execution time for the evaluation of finite element problems are found to be reduced considerably without compromising in the results mainly consist of accuracy of values and convergence rate.

Recently, many literature studies have focused on the development on new elements in finite elements. This paper aims to develop a new quadrature for the 3-node triangular element for the purpose of evaluation of element stiffness matrix. The analysis of triangular element is usually done in a quadrilateral element by dividing the quadrilateral element into two. The edge sampling point quadrature is a mimics of Gauss numerical integration scheme. This sampling integration scheme consists of five sampling points and weights where four sampling points are at the edge and one at the center of the element. Accuracy of results, convergence of the results and stability of values have been tested using the standard benchmarked problems defined by various research studies.

This research paper focuses on the objective of developing a quadrature for evaluating the element stiffness matrix for the four-node quadrilateral element in finite element analysis (FEA). The proposed integration scheme is defined as an element edge method (EEM), which mimics the Gauss numerical integration scheme. This integration scheme consists of five sampling points and weights where four integration point locations are at the edges and one is at the center of the quadrilateral element. The proposed quadrature scheme has been tested using various benchmarked problems designed by various researchers to study the convergence of the results, accuracy of results, and stability of values.

A new sampling point scheme with 13 evaluation points was introduced in this research study for 20-node brick elements. The new sampling points were located inside the brick element at the edges and the center point of the 20-node brick element. This integration scheme can be assumed to be an imitation of the Gaussian integration scheme. Standard benchmark problems were chosen from the different research works and compared with our proposed scheme. Finally, the proposed integration scheme achieves good results for 20-node brick elements on different performance parameters of finite element analysis.