Thermoelastic nonlinear bending of functionally graded porous sandwich beams using a hierarchical finite element formulation

Abstract This study examines the thermoelastic nonlinear bending behavior of sandwich beams through the development of an advanced finite element scheme. The structural model consists of isotropic face layers combined with a functionally graded porous (FGP) core, where two distinct porosity patterns are distributed along the thickness direction. To construct the nonlinear beam element, Timoshenko beam theory is adopted together with hierarchical shape functions, thereby avoiding the problem of shear locking. The proposed formulation accounts simultaneously for temperature variations and the temperature dependence of the constituent material properties. Nonlinear bending responses of sandwich beams subjected to either uniformly distributed loading or a concentrated force are determined using the Newton–Raphson iterative technique. The accuracy and computational efficiency of the presented model in predicting nonlinear responses of sandwich structures are validated. Furthermore, a parametric investigation is carried out to clarify the influences of porosity distribution, thermal effects, and support conditions on the nonlinear bending characteristics.