Material tailoring in three-dimensional flexural deformations of functionally graded material beams

Soft materials such as rubberlike and biological tissues are usually modeled incompressible. Mechanical properties of polymeric can be controlled either by exposing them to ultraviolet light for different time durations or changing their molecular structure. A challenge is find the spatial variation moduli fully utilize material. One way achieve this have a uniform distribution stress component likely cause failure. To this, we analytically analyze 3-dimensional infinitesimal flexural deformations functionally graded (FG) linearly elastic beam rectangular cross-section with Young’s modulus continuous function thickness coordinate. The problem first studied an incompressible material then compressible which Poisson’s ratio assumed constant. It found that when at point inversely proportional its distance from neutral axis, magnitude bending over beam’s cross-section, lightest possible deflections 2/3rd corresponding homogeneous has same maximum FG beam. Noting cannot infinity avoid assuming it constant small region around axis. For transversely isotropic beam, shown (2μ1 + μ2) determines stiffness where μ1 μ2 are, respectively, shear along perpendicular axis transverse isotropy. Beams having geometry depending upon whether beams deflection, total strain energy deformation.