scholarly journals A locking-free meshfree method for the simulation of shear-deformable plates based on a mixed variational formulation

2012 ◽  
Vol 241-244 ◽  
pp. 311-322 ◽  
Author(s):  
J.S. Hale ◽  
P.M. Baiz
Keyword(s):  
Variational Formulation ◽  
Meshfree Method ◽  
Mixed Variational Formulation ◽  
Shear Deformable ◽  
Shear Deformable Plates

Microstructural Size Dependency in Nonlinear Lateral Stability of Random Reinforced Microshells via Meshfree-Based Applied Mathematical Modeling

2021 ◽  
pp. 2150164
Author(s):  
Jie-Hua Sun ◽  
Zhi-Dong Zhou ◽  
Saeid Sahmani ◽  
Babak Safaei
Keyword(s):  
Research Work ◽  
Meshfree Method ◽  
Resin Matrix ◽  
Small Scale ◽  
Lateral Stability ◽  
Computational Framework ◽  
Probabilistic Technique ◽  
Prime Objective ◽  
Shear Deformable

The prime objective of this research work is to develop an efficient small scale-dependent computational framework incorporating microstructural tensors of dilatation gradient, rotation gradient, and deviatoric stretch gradient to analyze nonlinear lateral stability of cylindrical microshells. The numerical strategy is established based upon a mixed formation of the third-order shear deformable shell model and modified strain gradient continuum mechanics. The graphene nanoplatelet reinforcements are assumed to be randomly dispersed in a checkerboard scheme within the resin matrix. Accordingly, to extract the effective material properties, the Monte Carlo simulation together with a probabilistic technique are employed. The numerical solution for the microstructural-dependent nonlinear problem is carried out via the moving Kriging meshfree method having the capability to accommodate accurately the essential boundary conditions using proper moving Kriging shape function. It is represented that the role of the stiffening characters related to the effect of microstructural dilatation gradient, rotation gradient, and deviatoric stretch reduces continuously by going to deeper territory of the load-deflection stability path. Moreover, it is indicated that among various microstructural gradient tensors, the stiffening character of the rotation gradient is higher than deviatoric stretch gradient, and the stiffening character of the latter is more considerable than the dilatation gradient tensor.

A mixed variational formulation for a class of contact problems in viscoelasticity

2017 ◽  
Vol 97 (8) ◽  
pp. 1340-1356 ◽  
Author(s):  
A. Matei ◽  
S. Sitzmann ◽  
K. Willner ◽  
B. I. Wohlmuth
Keyword(s):  
Variational Formulation ◽  
Contact Problems ◽  
Mixed Variational Formulation

On Torsion and Transverse Flexure of Orthotropic Elastic Plates

1980 ◽  
Vol 47 (4) ◽  
pp. 855-860 ◽  
Author(s):  
E. Reissner
Keyword(s):  
Cross Section ◽  
Beam Theory ◽  
Bending Moment ◽  
Rate Of Change ◽  
Elastic Plates ◽  
Shear Center ◽  
Explicit Consideration ◽  
The Difference ◽  
Shear Deformable ◽  
Shear Deformable Plates

The equations of transverse bending of shear-deformable plates are used for the derivation of a system of one-dimensional equations for beams with unsymmetrical cross section, with account for warping stiffness, in addition to bending, shearing, and twisting stiffness. Significant results of the analysis include the observation that the rate of change of differential bending moment is given by the difference between torque contribution due to plate twisting moments and torque contribution due to plate shear stress resultants; a formula for shear center location which generalizes a result by Griffith and Taylor so as to account for transverse shear deformability and end-section warping restraint; a second-order compatibility equation for the differential bending moment; a contracted boundary condition of support for unsymmetrical cross-section beam theory in place of an explicit consideration of the warping deformation boundary layer; and construction of a problem where the effect of the conditions of support of the beam is such as to give noncoincident shear center and twist center locations.

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