Stability of a slender beam-column with locally varying Young? modulus

A locally varying temperature field or a mixture of two or more different materials can cause local variation of elasticity properties of a beam. In this paper, a new Euler-Bernoulli beam element with varying Young? modulus along its longitudinal axis is presented. The influence of axial forces according to the linearized 2nd order beam theory is considered, as well. The stiffness matrix of this element contains the transfer constants which depend on Young? modulus variation and on axial forces. Occurrence of the polynomial variation of Young? modulus has been assumed. Such approach can be also used for smooth local variation of Young? modulus. The critical loads of the straight slender columns were studied using the new beam element. The influence of position of the local Young? modulus variation and its type (such as linear, quadratic, etc.) on the critical load value and rate of convergence was investigated. The obtained results based on the new beam element were compared with ANSYS solutions, where the number of elements gradually increased. Our results show significant influence of the locally varying Young? modulus on the critical load value and the convergence rate.