Enhanced geometrically-nonlinear poro-FG shear-deformable beams under moving load in discrete state-space

Using Hamilton's principle, the motion-governing partial differential equations of enhanced geometrically-nonlinear porous functionally-graded beam subjected to a concentrated moving force were derived and compared with the corresponding geometrically-nonlinear beam. The beam density and elastic modulus vary continuously along the web direction from those of metal to those of ceramic. The motion-governing difference equations were achieved via generalized differential quadrature and the Newmark's methods, assembled via state-spatial variables and their velocities, and solved via Newton-Raphson stabilized iterations. Components of the beam dynamic elastica, shearing force and flexural moment were obtained along the span. Proportionality of nonporous-FG beam deflection, to porosity, to material parameter, and to metal portion vis-a-vis ceramic, and that of poro-FG beamanti-symmetry in deflection, to load speed was revealed. The critical speed of the load that causes the locally-greatest displacements was found. Cross-sectional shearing and normal stresses were obtained at mid-span, across the web. As a particular case, the beam motion-governing difference equations were reduced to equilibrium-governing ones and solved. The lateral displacement of the beam static elastica was compared with that of the corresponding nonlinear and linear beams.