2025 , Volume 30, № 1, p.24-40

The paper addresses the problem of dynamic response of a curvilinear rod fabricated of a functionally graded material subjected to thermal shock. To solve the problem, geometrically nonlinear finite element is formulated using the concept of kinematic group, thus the necessary convergence criterion for the solution is satisfied authomatically. As a reference line of the rod, we use the line that passes through the cross-sectional center of mass. The shape functions of the rod finite elementare constructed using the exact analytical solution for the bending problem of the Timoshenko beam. Based on these shape functions, the finite-element model avoids the shear locking issue when analyzing bending of thin rods. To compute the nodal thermal loads and stiffness of the rod, the unsteady heat-conduction problem is solved using a numerical procedure that accounts temperature dependent properties of the material. Nonlinear equations of motion of the finite-element model are numerically integrated in the time domain in a step-by-step manner using the implicit Newmark method. At each time step, the deformed configuration of the rod is determined using the Newton–Raphson iterative technique. The algorithm proposed is implemented in a Fortran computer code and tested using sample problems. The accuracy of the solution is supported by comparison to numerical data available in literature. Structural dynamic response of FGM beams and shallow arches is studied. The effect of initial geometric imperfections, boundary conditions, grading index, and magnitude of thermal loading on dynamic response of the rods is examined and discussed.