A general method for analyzing moderately large deflections of a non-uniform beam: an infinite Bernoulli-Euler-von Karman beam on a nonlinear elastic foundation

作者：Jang T S^*

来源：Acta Mechanica, 2014, 225(7): 1967-1984.

DOI：10.1007/s00707-013-1077-x

The present paper concerns a semi-analytical procedure for moderately large deflections of an infinite non-uniform static beam resting on a nonlinear elastic foundation. To construct the procedure, we first derive a nonlinear differential equation of a Bernoulli-Euler-von Karman %26quot;non-uniform%26quot; beam on a %26quot;nonlinear%26quot; elastic foundation, where geometrical nonlinearities due to moderately large deflection and beam non-uniformity are effectively taken into account. The nonlinear differential equation is transformed into an equivalent system of nonlinear integral equations by a canonical representation. Based on the equivalent system, we propose a method for the moderately large deflection analysis as a general approach to an infinite non-uniform beam having a variable flexural rigidity and a variable axial rigidity. The method proposed here is a functional iterative procedure, not only fairly simple but straightforward to apply. Here, a parameter, called a base point of the method, is also newly introduced, which controls its convergence rate. An illustrative example is presented to investigate the validity of the method, which shows that just a few iterations are only demanded for a reasonable solution.

• 出版日期2014-7