Exact Static Analysis of In-Plane Curved Timoshenko Beams with Strong Nonlinear Boundary Conditions (original) (raw)
2015, Mathematical Problems in Engineering
Analytical solutions have been developed for nonlinear boundary problems. In this paper, the shifting function method is applied to develop the static deflection of in-plane curved Timoshenko beams with nonlinear boundary conditions. Three coupled governing differential equations are derived via the Hamilton’s principle. The mathematical modeling of the curved beam system can be decomposed into a complete sixth-order ordinary differential characteristic equation and the associated boundary conditions. It is shown that the proposed method is valid and performs well for problems with strong nonlinearity.
Related papers
On Exact Analytical Solutions of the Timoshenko Beam Model Under Uniform and Variable Loads
2021
In this research work, we consider the mathematical model of the Timoshenko beam (TB) problem in the form of a boundary-value problem of a system of ordinary differential equations. Instead of numerical solution using finite difference and finite volume methods, an attempt is made to derive the exact analytical solutions of the model with boundary feedback for a better and explicit description of the rotation and displacement parameters of the TB structure model. The explicit analytical solutions have been successfully found for the uniform and real-time variable load cases. The rotation and displacement profiles obtained through the analytical solutions accurately picture the structure of the beam under uniform and variable loads.
On the Derivation of Exact Solutions of a Tapered Cantilever Timoshenko Beam
Civil Engineering Dimension
A tapered beam is a beam that has a linearly varying cross section. This paper presents an analytical derivation of the solutions to bending of a symmetric tapered cantilever Timoshenko beam subjected to a bending moment and a concentrated force at the free end and a uniformly-distributed load along the beam. The governing differential equations of the Timoshenko beam of a variable cross section are firstly derived from the principle of minimum potential energy. The differential equations are then solved to obtain the exact deflections and rotations along the beam. Formulas for computing the beam deflections and rotations at the free end are presented. Examples of application are given for the cases of a relatively slender beam and a deep beam. The present solutions can be useful for practical applications as well as for evaluating the accuracy of a numerical method.
Loading Preview
Sorry, preview is currently unavailable. You can download the paper by clicking the button above.