Samir Al-Sadder

Exact Large Deflection Analysis of Nonprismatic Cantilever Beams of Nonlinear Bimodulus Material Subjected to Tip Moment

This paper presents an exact solution for large deflection behavior of nonprismatic cantilever beams of nonlinear bimodulus type material and subjected to tip concentrated moment. The highly nonlinear simultaneous first-order differential equations were solved analytically using the power series approach. Several numerical examples are carried out to investigate the effect of bimodulus properties, material parameter, n, and the applied tip moment on the large deflection behavior of nonprismatic cantilever beams. The numerical results show that the interaction (i.e., coupling) between the bimodulus material properties, the material constant, n, and the applied tip moment, plays a significant role on the large deflection behavior of cantilever beams. A comparative study with ADINA has been made to verify the accuracy of the presented analytical solution, and excellent agreement has been obtained.

A Proposed Technique for Large Deflection Analysis of Cantilever Beams Composed of Two Nonlinear Elastic Materials Subjected to an Inclined Tip Concentrated Force

A new technique was proposed for the large deflection problem of a prismatic composite cantilever beam made of two different nonlinear elastic materials and subjected to an inclined tip concentrated force. Two types of composite cantilever beams were considered in this study: A solid rectangular and a hollow circular cross-section beam. The proposed technique assumes that the behavior of a composite cantilever beam is equivalent to the behavior of two homogeneous cantilever beams. A semi-analytical solution describing the complete behavior of each homogeneous beam was derived and the complete deflection curve of the composite cantilever beam was obtained by considering the weighted average deflection curves of the two homogeneous cantilevers with respect to the tip forces. Several numerical examples were presented at the end of the study. Results obtained using the proposed technique were compared with results obtained using the software ADINA and found to be in good agreement.

A New Quasi-Linearization Finite Difference Scheme for Large Deflection Analysis of Prismatic and Non-Prismatic Inextensible Slender Beams

A new scheme called quasi-linearization finite differences is developed for large deflection analysis of prismatic and non-prismatic inextensible slender beams with different boundary conditions subjected to various types of continuous and discontinuous external loads in horizontal and vertical global directions. Simultaneous equations of highly nonlinear and linear terms are obtained when casting the derived exact highly nonlinear governing differential equation using central finite differences on the nodes along the beam. A quasi-linearization scheme is used to solve these equations based on successive corrections of the nonlinear terms in the simultaneous equations. The nonlinear terms in the simultaneous equations are assumed constant during each correction (iteration). Several representative numerical examples of prismatic and non-prismatic slender beams with different loading and boundary conditions are analyzed to illustrate the merits of the new adopted numerical scheme as well as its validity, accuracy and efficiency. The results of the present scheme are checked using large displacement finite element analysis of MSC/NASTRAN program. A comparison between present scheme and MSC/NASTRAN results reveals excellent agreements. The advantage of the new scheme is that the load can be applied in one step with few iterations (3 to 6 iterations).

An Accurate Numerical Scheme for Large Deflection Analysis of Non-Prismatic Inextensible Slender Beams Subjected to General Loading and Boundary Conditions

This paper studies the large deflection behavior of prismatic and non-prismatic inextensible beams subjected to various types of loading and boundary conditions. The formulation is based on representing the angle of rotation by a power series and substituting it into the derived governing nonlinear differential equation. The coefficients of the power series are obtained by minimizing the integral of the residual error over the deflected beam axis. Several numerical examples are presented covering prismatic and non-prismatic beams subjected to uniform and non-uniform distributed loads. A large displacement finite element analysis using the package MSC/NASTRAN was used to check the accuracy and efficiency of the present numerical method. Excellent agreement was observed between the two numerical schemes.