Shear Lag Analysis due to Flexure of Prismatic Beams with Arbitrary Cross-Sections by FEM

This paper presents the use of a finite element method (FEM) to analyze the shear lag effect due to the flexure of beams with an arbitrary cross-section and homogeneous elastic material. Beams are constrained by the most common types of supports, such as fixed, pinned, and roller. The transverse, concentrated, or distributed loads act on the beams through the shear center of the cross-section. The presented FEM transforms the 3D analysis of the shear lag phenomenon into separated 2D cross-sectional and 1D beam modeling. The characteristics of the cross-section are firstly derived from 2D FEM, which uses a 9-node isoparametric element. Then, a 1D FEM, which uses a linear isoparametric element, is developed to compute the deflection, rotation angle, bending warping parameter, and stress resultants. Finally, the stress field is obtained from the local analysis on the 2D-cross section. A MATLAB program is executed to validate the numerical method. The validation examples have proven the efficiency and reliability of the numerical method for analyzing shear lag flexure, which is a common problem in structural design.

Isoparametric Element Analysis of Two-Dimensional Unsaturated Transient Seepage

A FEM for unsaturated transient seepage is established by using a quadrilateral isoparametric element, considering the fact that the main permeability does not coincide with the axis situation. It creates a function by using the element’s node hydraulic head and shape function instead of the real head in the Richard seepage control equation. With the help of the Galerkin weighted residual method, a FEM equation is given for analyzing 2-dimensional transient seepage problem. Further, based on the Jacobi matrix and Gauss numerical integral, it determines the elements of stiffness and capacitance matrices. This FEM equation considers not only the anisotropic of soil but also the uncoincidence between permeability and the axis. It is a common form of transient seepage. In the end, two examples illustrate the node accuracy of the quadrilateral element and the correctness of this FEM equation.

Numerical Solution of Prestressed Foundation - Subsoil Interaction Using FEM

This paper deals with prestressed foundation - soil interaction. For interaction task is used FEM model of thick slab with shear influence which is supported by structural strength modified elastic half-space. The calculation of deformations, internal forces and contact stresses in subsoil is performed iteratively by means of isoparametric element and numerical integration. The results of settlement and stress of non-prestressed/prestressed slab - subsoil interaction are compared on example.

Numerical model of time-dependent diffusion of chlorides in the concrete based on 2D four-node isoparametric element

The enhancement of 2D model for the diffusion of chloride ions into reinforced concrete considering the time-dependent diffusion coefficient is discussed in the article. The non-stationary Finite Element Model is based on the four-node isoparametric element. The algorithm is implemented in MatLab compatible environment and an important part of source code is presented. The results of Finite Element Analysis are compared with the results of 2D analytical diffusion model.

On Finite Element Computations of Contact Problems in Micropolar Elasticity

Within the linear micropolar elasticity we discuss the development of new finite element and its implementation in commercial software. Here we implement the developed 8-node hybrid isoparametric element into ABAQUS and perform solutions of contact problems. We consider the contact of polymeric stamp modelled within the micropolar elasticity with an elastic substrate. The peculiarities of modelling of contact problems with a user defined finite element in ABAQUS are discussed. The provided comparison of solutions obtained within the micropolar and classical elasticity shows the influence of micropolar properties on stress concentration in the vicinity of contact area.

Dynamic Inhomogeneous Isoparametric Element with Coordinate Transformation

Based on the coordinate transformation method, the formula of the dynamic inhomogeneous isoparametric finite element method is presented for generating element stiffness, damping and mass matrices. First, the global coordinate form and simplified form of dynamic inhomogeneous finite element are given in this paper. Then, the discrete material parameter distributions under the isoparametric coordinate system are obtained by using the transformation relationship between the global coordinates and the isoparametric coordinates. The simplified form with the discrete material parameter distributions is obtained for generating the element stiffness and mass matrices of the dynamic inhomogeneous isoparametric element. The numerical examples show that the scheme proposed in present paper has high precision.