Abstract:
As a simplified model of three-dimensional elasticity theory, the predictive accuracy and applicable boundary of one-dimensional beam theory must be rigorously examined and clarified when dealing with functionally graded porous materials (FGPMs) with significant inhomogeneous properties. This study systematically evaluates the effectiveness and accuracy of four widely-adopted beam theories in the literature, namely the classical beam theory (CBT), first-order shear deformation beam theory (FSDBT), third-order shear deformation beam theory (TSDBT), and trigonometric shear deformation beam theory (BSDBT), for the bending problem of functionally graded porous beams. Three common porosity gradient distributions (FGX, FGO, UD) were considered, and it was assumed that material properties vary continuously along the thickness direction. According to the principle of minimum total potential energy, the governing differential equations for different beam theories were derived, and the numerical solutions for the bending problem of functionally graded porous beams were obtained using the differential quadrature method. By comparing the calculated results with finite element simulation ones, the effectiveness and accuracy of different beam theories in studying the bending problem of functionally graded porous beams were examined. Parametric studies were then conducted to discuss the influences of porosity gradient and coefficient, aspect ratio, and boundary conditions on the difference between theoretical predictions and simulation results, and the underlying reasons for the differences were analyzed. Results show that for the FGX porous beams of high porosity, the difference increases significantly as the porosity coefficient and constraint stiffness increase, while it decreases as aspect ratio increases. When the porosity coefficient exceeds 0.9 or the aspect ratio is less than 20, the four beam theories are all unable to accurately describe the deformation of the cross-section of FGX porous beams, and the theoretical predictions are no longer reliable. For such cases, it is recommended to employ 3D elasticity theory/finite element simulation to obtain precise solutions, or alternatively develop a more refined beam theory specifically adapted for functionally graded porous materials to ensure the computational reliability.