A refined shear deformation theory for flexure of thick beams

Abstract

A Hyperbolic Shear Deformation Theory (HPSDT) taking into account transverse shear deformation effects, is used for the static flexure analysis of thick isotropic beams. The displacement field of the theory contains two variables. The hyperbolic sine function is used in the displacement field in terms of thickness coordinate to represent shear deformation. The transverse shear stress can be obtained directly from the use of constitutive relations, satisfying the shear stress-free boundary conditions at top and bottom of the beam. Hence, the theory obviates the need of shear correction factor. Governing differential equations and boundary conditions of the theory are obtained using the principle of virtual work. General solutions of thick isotropic simply supported, cantilever and fixed beams subjected to uniformly distributed and concentrated loads are obtained. Expressions for transverse displacement of beams are obtained and contribution due to shear deformation to the maximum transverse displacement is investigated. The results of the present theory are compared with those of other refined shear deformation theories of beam to verify the accuracy of the theory.

Accuracy of Individual Trabecula Segmentation Based Plate and Rod Finite Element Models in Idealized Trabecular Bone Microstructure

“…While the rod-predominant structure exists in extremely osteoporotic trabecular bone, the trabecular thickness is approximately 100 lm on average at the distal tibia and radius [27], in which case the PR model provided an accurate estimation of the Young's modulus and yield strength, similar to those for plate-rod structures. The deviation of the PR model predictions from the voxel model in the thick rod-rod structure was partly caused by the limitation of the beam theory, such as the shear deflection effects at a low beam length-to-thickness ratio [28]. Although we have examined the elastic-plastic behaviors of the trabecular bone model, this approach could be applicable to other nonlinear phenomena such as viscoelastic simulations.…”

The Unified Solution for a Beam of Rectangular Cross-Section with Different Higher-Order Shear Deformation Models

“…see Ghugal and Sharma, 2011), so, from the first of Eqs. (1), in terms of ϕ, the moment can be further expressed as…”

Plane elasticity solutions for beams with fixed ends

“…In addition, some special finite elements (Heyliger and Reddy, 1988;Kant and Gupta, 1988) were also constructed by considering normal strains and shear strains through the thickness of the beam. A similar assumption of the shear strain can be further used to analyze the dynamic response of the curved beam (Bhimaraddi, 1988) and the static flexure of thick isotropic beams (Ghugal and Sharma, 2011).…”