Mehdi Aminbaghai

Effect of Non-Uniform Torsion on Elastostatics of a Frame of Hollow Rectangular Cross-Section

Abstract In this paper, results of numerical simulations and measurements are presented concerning the non-uniform torsion and bending of an angled members of hollow cross-section. In numerical simulation, our linear-elastic 3D Timoshenko warping beam finite element is used, which allows consideration of non-uniform torsion. The finite element is suitable for analysis of spatial structures consisting of beams with constant open and closed cross-sections. The effect of the secondary torsional moment and of the shear forces on the deformation is included in the local finite beam element stiffness matrix. The warping part of the first derivative of the twist angle due to bimoment is considered as an additional degree of freedom at the nodes of the finite elements. Standard beam, shell and solid finite elements are also used in the comparative stress and deformation simulations. Results of the numerical experiments are discussed, compared, and evaluated. Measurements are performed for confirmation of the calculated results.

ELASTOSTATIC AND MODAL AND BUCKLING ANALYSIS OF SPATIAL FGM BEAM STRUCTURES

In this contribution, a homogenized beam finite element of double symmetric crosssection made of a Functionally Graded Material (FGM) is presented, which can be used for static, modal and buckling analysis of single beams and beam structures with three directional variation of material properties. The material properties in a real beam can vary continuously in longitudinal direction while the variation with respect the transversal and lateral directions is assumed to be symmetric in a continuous or discontinuous manner. The shear force deformation effect and the effect of inertia and rotary inertia are taken into account. Additionally, the longitudinally varying Winkler elastic foundation and the effect of axial force are included by the finite element equations as well. Homogenization of spatially varying material properties to effective quantities with a longitudinal variation is done by the extended mixture rules and multilayer method (MLM). For the homogenized beam the 1212 finite element effective matrix, consisting of the linearized stiffness and consistent mass inertia terms, is established. Numerical experiments are made concerning static, modal and buckling analyses of single FGM beam and beam structures to show the accuracy and effectiveness of the proposed FGM beam finite element.

NUMERICAL SOLUTION OF DIFFERENTIAL EQUATIONS WITH NON-CONSTANT COEFFICIENTS

Abstract. Nowadays, new materials like Functionally Graded Material (FGM) are necessary for sophisticated structures like MEMS systems, advanced electronic devices, etc. Computer modelling of such complex systems, like structures with spatial variation of material properties (e.g. FGM) are, using commercial FEM code with classic elements, needs remarkable effort during preparation phase and sufficient computer equipment for solution phase because of necessity the numbers of elements and material models. Therefore new methods for modeling and simulation of FGM beams with spatial variation of material properties are developed. In the proposed contribution, semi-analytical method (based on calculation of transfer functions and transfer constants) for solution of differential equation with non-constant polynomial coefficients, is presented. This method is used in derivation process (for setting up the transfer matrix) of our new beam finite elements for modeling and simulation of Functionally Graded Material (FGM) beam structures (e.g. new 3D FGM beam finite element for modal and structural analysis, new FGM beam finite elements for coupled electro-thermo-mechanical analysis). Numerical experiments are made to show the accuracy and effectiveness of this method.

MODELLING OF WARPING EIGENVIBRATION BY NON-UNIFORM TORSION

This contribution contains a novel investigation of the influence of warping of the cross-section of twisted beams on their eigenvibrations. The investigation is based on the analogy of the bending beam theory and the non-uniform torsion theory of thin-walled open and closed cross-sections. Based on them, the differential equations for dynamic loads, considered as equivalent static loads, are presented. The effect of the secondary torsion moment deformation is taken into account. A part of the first derivative of the twist angle is taken as a warping degree of freedom. The solution of this differential equation is then used for setting up the transfer matrix. The numerical investigation contains the analysis of the natural frequencies and mode shapes of straight cantilever beams with and without consideration of the influence of warping of the cross-section. Beams with open and closed cross-sections are considered. Obtained results are compared with the ones calculated by standard solid and warping beam finite elements.

Exact Solution of Bending Free Vibration Problem of the FGM Beams with Effect of Axial Force

In this contribution a fourth-order differential equation of the functionally graded material (FGM) beam deflection with longitudinal variation of the effective material properties has been derived where the second order beam theory has been applied for establishing the equilibrium- and kinematics beam equations. Not only the shear forces deformation effect and the effect of consistent mass distribution and mass moment of inertia but also the effect of large axial force has been taken into account. Numerical experiments will be done concerning the calculation of the eigenfrequencies and corresponded eigenmodes of chosen one-layer beams and multilayered FGM sandwich beams. Effect of the axial forces on the free vibration has been studied and evaluated. The solution results will be compared with those obtained by using a very fine mesh of 2D plane elements of the FEM software ANSYS.