On Timoshenko-like modeling of initially curved and twisted composite beams

Deformation analysis of functionally graded beams by the direct approach

“…We observe that all the boundary conditions are satisfied by the field (31), and the equations of motion reduce to t …”

“…Assume that q à has a symmetrical distribution in the x 1 direction: q à (x 1 , x 2 ) = q à ( x 1 , x 2 ). We search for a solution in the form (31). Then the boundary conditions (30) are satisfied and the equations of motion reduce to…”

External fixator configurations in tibia fractures: 1D optimization and 3D analysis comparison

“…This finite element is integrated in the FEAP library [29]. The finite element methodology developed has enabled us to obtain the properties associated with the numerical modeling of beams with arbitrary material and cross-section geometry, in which the element stiffness is computed on the bases of the variational asymptotic method presented by Yu et al [30]. Therefore, the beam constitutive relation is computed by VABS routines library which were already integrated in the FEAP program by authors at previous work [12].…”

Timoshenko Beam Element With Anisotropic Cross-Sectional Properties

“…Theories for determining the cross-section stiffness matrix have been presented by e.g. Giavotto et al [1] and Yu et al [2]. The method by Giavotto et al invokes the virtual work per unit beam length to obtain a linear system of second-order differential equations with constant coefficients that have a homogeneous and particular solution.…”