Physical Nonlinear Mechanical Behavior Of Foamed Metal Beams

The physical nonlinear mechanic behavior of foamed metal beam is investigated in this paper.The problem is solved numerically by assuming that the modulus of the material is a linear function of strain.The effects of nonlinear parameters of constitutive relation,external loads,boundary conditions on the bending deformation and the neutral layer of the beam are discussed in detail and the influence of nonlinear parameters of constitutive relation on the critical load of the compression rods are also considered too.The main contents can be summarized as follows:1)Based on classical beam theory and nonlinear constitutive relation,the basic equations of beam bending problem under nonlinear constitutive relation are derived by considering the effects of transverse distribution load.With the given corresponding boundary conditions,the small deflection bending problem and large deflection bending problem of foamed metal beam under different boundary conditions are solved numerically by shooting method after dimensionless.The effects of the non-linear parameters of the constitutive relation,boundary constraints,external loads on the bending deformation and the neutral layer of the beam are analyzed.By numerical results we can know that the deformations of small deflection and large deflection are same when the beams are not subjected to axial restraint.The bending stiffness of the beams decreases with the increasing of the absolute value of the non-linear parameterE_rof the constitutive relationship.The position of the neutral layer on the geometric middle plane is reversed with different sign ofE_r.For beam whose axial displacement is constrained,because of the generation of axial force during the process of deformation,the bending stiffness increases with the increasing ofE_r.WhenE_r?0,the limit load will appear and the equilibrium configuration beyond the limit load does not exist;whenE_ris positive number and negative number,the neutral layer is opposite to the geometric midplane.In the large deflection problem,due to the influence of geometric nonlinearity,none limit load is found in the numerical calculation,and the position of the neutral layer will not be reversed with respect to the geometric midplane due to the changing of positive and negative numbers ofE_r.When the constitutive relationship is non-linear,the solution of the large deflection problem can more accurately reflect the deformation of the beam which known from numerical results.2)It is found that the critical load decreases with the increase of constitutive nonlinear parameters by analyzed the influence of constitutive nonlinear parameterE_r on critical load of metal foam rods.