Explicit Solution to Large Deformation of Cantilever Beam by Improved Homotopy Analysis Method II: Vertical and Horizontal Displacements

Ludwick Cantilever Beam in Large Deflection Under Vertical Constant Load

The aim of this paper is to calculate the horizontal and vertical displacements of a cantilever beam in large deflections. The proposed structure is composed with Ludwick material exhibiting a different behavior to tensile and compressive actions. The geometry of the cross-section is constant and rectangular, while the external action is a vertical constant load applied at the free end. The pro...

Vibration Analysis of a Nonlinear Beam Under Axial Force by Homotopy Analysis Method

In this paper, Homotopy Analysis Method is used to analyze free non-linear vibrations of a beam simply supported by pinned ends under axial force. Mid-plane stretching is also considered for dynamic equation extracted for the beam. Galerkin decomposition technique is used to transform a partial dimensionless nonlinear differential equation of dynamic motion into an ordinary nonlinear differenti...

On the Corotational Beam Element Formulation in Large Deformation Analysis

This paper sheds more light on the co-rotational element formulation for beams with uniform cross-section. The co-rotational elements are commonly used in problems in which a structure undergoes a large deformation. In this study, the foregoing element obeys the Euler-Bernoulli beam assumptions. Unlike the formulations presented in the literature, in this paper, a number of local nodal coordina...

On the Analytical Solution of Kirchhoff Simplified Model for Beam by using of Homotopy Analysis Method

In this paper the problem of Kirchhoff simplified model for beam is studied and analytical solution is presented. Governing equation is solved analytically using a kind of analytic technique for nonlinear problems namely the Homotopy Analysis Method (HAM), for the first time. Present solution gives an expression which can be used in wide range of time for all domain of response and method is ab...

Numerical Solution of Fuzzy Linear Volterra Integral Equations of the Second Kind by Homotopy Analysis Method