Thermal Stress Analysis for Bi-modulus Foundation Beam under Nonlinear Temperature Difference
It is shown that many materials in practical engineering have different moduli in tension and compression. Especially, graphene, a magical material with the highest strength, is a kind of bi-modulus material. In this paper, mechanical response of bi-modulus Winkler foundation beam under nonlinear temperature distribution along height of the beam is studied. A new and convenient method, “intersecting line criterion”, is proposed to certify number of neutral axis in foundation beam and governing equation (set) of position of neutral axis is established, which is solved by iteration procedure of Newton’s method in Matlab. Semi-analytical solutions of stress, deflection and bending moment are subsequently obtained. Meanwhile, a finite element calculation procedure for calculating the temperature stress in bi-modulus structures is developed. Return the analytical solution to the result of the same modulus theory, and compare the analytical solution with finite element procedure solution and common finite element software Abaqus simulation solution. It shows that both of semi-analytical solution and calculation procedure proposed are reliable to use. Finally, discrepancies between nonlinear temperature effect and linear temperature and external force effect are discussed, which may supply some suggestions for calculation and optimization of such structures and members.