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.

Signal Propagation in Soil Medium: A Two Dimensional Finite Element Procedure

A two-Dimensional Finite Element Method of electromagnetic (EM) wave propagation through the soil is presented in this chapter. The chapter employs a boundary value problem (BVP) to solve the Helmholtz time-harmonic electromagnetic model. An infinitely large dielectric object of an arbitrary cross-section is considered for scattering from a dielectric medium and illuminated by an incident wave. Since the domain extends to infinity, an artificial boundary, a perfectly matched layer (PML) is used to truncate the computational domain. The incident field, the scattered field, and the total field in terms of the z-component are expressed for the transverse magnetic (TM) and transverse electric (TE) modes. The radar cross-section (RCS), as a function of several other parameters, such as operating frequency, polarization, illumination angle, observation angle, geometry, and material properties of the medium, is computed to describe how a scatterer reflects an electromagnetic wave in a given direction. Simulation results obtained from MATLAB for the scattered field, the total field, and the radar cross-section are presented for three soil types – sand, loam, and clay.

Analytical Method to Interpret Displacement in Elastic Anisotropic Soil due to a Tunnel Cavity with an Arbitrary Cross Section

Based on complex variable theory and conformal mapping method, the paper presents full plane elastic solutions around an unlined tunnel with arbitrary cross section in anisotropic soil. The solutions describe soil elastic solutions for assuming that the displacement vectors along the tunnel boundary are directed towards the center of the tunnel. Tunnels with different cross sections are used to illustrate the method and its correctness. An elliptical unlined tunnel case is discussed in detail in the paper. Using the image method, an approximate solution for predicting surface displacement and subsurface horizontal displacement around an unlined tunnel in anisotropic soil can be obtained. The results show anisotropic stiffness properties n n = E h / E v and m m = G v h / E v have a great effect on the displacement distribution patterns around an elliptical tunnel with certain shape.

An analytical model of a rotating radial cantilever beam considering the coupling between bending, stretching and torsion

In this paper, the mode coupling between bending, stretching and torsional deformations is mainly studied by presenting an analytical model of a rotating cantilever beam with pre-twist angle and arbitrary cross section. Equations of motion of the beam are derived using Hamilton's principle. The Coriolis effect due to the coupling of the bending deformation and stretching deformation, the eccentricity caused by inconsistency between elastic center and centroid, spin softening effect, stress stiffening effect, shear deformation, and rotary inertia are included in the model. Equations of motion are solved by the Rayleigh-Ritz method. The natural frequencies obtained by the proposed analytical modal are in good agreement with those obtained by Finite Element Method (FEM) which proved the accuracy of the analytical model. Finally, the coupling between different mode components is studied in detail based on a quantitative method. The transformation/ conversion between different mode components is revealed, the influence of rotational speed, setting angle and pre-twist angle on this conversion mode is studied. Results show that a specific mode shape is usually composed of multiple mode components. The essence of mode coupling is the coupling between different mode components. The influence of rotational speed, setting angle and pre-twist angle on the mode coupling is that they cause the transformation/ conversion between different mode components.