This paper presents an analytical solution for the static analysis of thick laminated rectangular beams with clamped boundary conditions at either or both of the beam's edges. A unified formulation known as Carrera's Unified Formulation (CUF) is used in order to consider shear deformation theories of arbitrary order. The governing equations are obtained by using the principle of virtual work. The main novelty is the use of the boundary-discontinuous Fourier approach for laminated beams in the framework of a unified formulation. Unlike Navier-type solutions, the present development can obtain analytical solutions for beams with clamped boundary conditions. A 3D finite element solution is used to validate the obtained results. The present theory can analyze clamped beams accurately so benchmark results are provided.

This paper presents an analytical solution for static analysis of thick rectangular beams with different boundary conditions. Carrera's Unified Formulation (CUF) is used in order to consider shear deformation theories of arbitrary order. The novelty of the present work is that a boundary discontinuous Fourier approach is used to consider clamped boundary conditions in the analytical solution, unlike Navier-type solutions which are restricted to simply supported beams. Governing equations are obtained by employing the principle of virtual work. The numerical accuracy of results is ascertained by studying the convergence of the solution and comparing the results to those of a 3D finite element solution. Beams subjected to bending due to a uniform pressure load and subjected to torsion due to opposite linear forces are considered. Overall, accurate results close to those of 3D finite elemen...

We introduce a compact and unified shear deformation theory for plates with elasto-plastic behavior. We formulate the kinematics of the two-dimensional structure in a compact and unified manner using the Carrera Unified Formulation. This formulation allows for generalized expansions of the primary variables and through-the-thickness functions. We obtain the governing equations using the principle of virtual work and a finite element discretization. We solve the nonlinear equations using a Newton–Raphson linearization scheme, and linearize the constitutive equations using the algorithmic tangent moduli. We consider the J2 flow theory of plasticity, and use a backwards Euler scheme to update the stresses. We analyze the convergence, and compare the effectiveness of the Mixed Interpolation of Tensorial Components technique in contrasting the shear locking phenomenon in the nonlinear regim...

This paper presents the development and validation of a tridimensional 7-DOF human body model for the representation and study of closed kinetic chain exercises (CKCE) performed with the feet fixed in space, i.e. low posture exercises. The biomechanical model, a link-segment model, is based on an Euler-Lagrange formulation and employs a generalized joint coordinate system. A top-down mechanical analysis provides an estimation of the internal joint moments, along with the vertical ground reaction forces, using kinematical data collected by inertial sensors. The model is validated by correlating estimated ground reaction forces to kinetic experimental data from force plates. Pearson correlation coefficients were calculated for four CKCE types (150 trials in total). In all cases, a median correlation r > 0.90 was found, hence proving that the proposed model is quite satisfactory for CKCE mo...