The Study of the Size-Dependent Geometrically Nonlinear Bernoulli-Euler Beam in the Temperature Field Impacted by the Transversal Load

摘要

The paper investigates a mathematical model of the motion of a component of the flexible physically-nonlinear single-layer size-dependent beam under the stationary temperature field, taking into account the Euler-Bernoulli hypotheses. The initial differential equations are derived from the variation principles. The temperature distribution across the thickness is defined by solving the two dimensional Laplace equation for the corresponding boundary conditions. The algorithm was developed in order to solve the resulting equations using the finite difference method and Runge-Kutta method. Convergence of the numerical methods is investigated, and validity of the results is provided. A new buckling phenomenon applied for dissipative systems is found under the influence of the temperature field and time infinite load.