Refined Mindlin–Reissner theory of forced vibrations of shear deformable plates

2011 ◽  
Vol 33 (1) ◽  
pp. 265-272 ◽  
Author(s):  
Milan Batista
Keyword(s):  
Forced Vibrations ◽  
Reissner Theory ◽  
Shear Deformable ◽  
Shear Deformable Plates

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.

A GALERKIN MESHFREE METHOD WITH STABILIZED CONFORMING NODAL INTEGRATION FOR GEOMETRICALLY NONLINEAR ANALYSIS OF SHEAR DEFORMABLE PLATES

2011 ◽  
Vol 08 (04) ◽  
pp. 685-703 ◽  
Author(s):  
DONGDONG WANG ◽  
YUE SUN
Keyword(s):  
Nonlinear Analysis ◽  
Large Deflection ◽  
Lagrangian Description ◽  
Geometrically Nonlinear ◽  
Geometrically Nonlinear Analysis ◽  
Nodal Integration ◽  
Galerkin Meshfree ◽  
Shear Deformable ◽  
Shear Deformable Plates ◽  
Stabilized Conforming Nodal Integration

A Galerkin meshfree approach formulated within the framework of stabilized conforming nodal integration (SCNI) is presented for geometrically nonlinear analysis of large deflection shear deformable plates. This method is based upon a Lagrangian curvature smoothing in which the smoothed curvature is constructed within a nodal representative domain on the initial configuration. It is shown that the Lagrangian smoothed nodal gradients of the meshfree shape function is capable of exactly representing arbitrary constant curvature fields in the discrete sense of nodal integration. The consistent linearization is performed on the weak form of large deflection plate in the context of the total Lagrangian description. Subsequently, the discrete incremental equations are obtained by the method of SCNI in which to relieve the locking as well as ensure the stability of the present scheme, the bending contribution is evaluated using the smoothed nodal gradients, while the membrane and shear contributions are computed with the direct nodal gradients. The effectiveness of the present method is thoroughly demonstrated through several numerical examples.

Isogeometric boundary integral formulation for Reissner’s plate problems

2019 ◽  
Vol 37 (1) ◽  
pp. 21-53
Author(s):  
Ahmed K. Abdelmoety ◽  
Taha H.A. Naga ◽  
Youssef F. Rashed
Keyword(s):  
Singular Integrals ◽  
Boundary Integral ◽  
Element Formulation ◽  
Analysis Tool ◽  
Content Type ◽  
Nurbs Curves ◽  
Generalized Displacements ◽  
Spline Basis ◽  
Shear Deformable ◽  
Shear Deformable Plates

Purpose This paper aims to develop a new isogeometric boundary element formulation based on non-uniform rational basis splines (NURBS) curves for solving Reissner’s shear-deformable plates. Design/methodology/approach The generalized displacements and tractions along the problem boundary are approximated as NURBS curves having the same rational B-spline basis functions used to describe the geometrical boundary of the problem. The source points positions are determined over the problem boundary by the well-known Greville abscissae definition. The singular integrals are accurately evaluated using the singularity subtraction technique. Findings Numerical examples are solved to demonstrate the validity and the accuracy of the developed formulation. Originality/value This formulation is considered to preserve the exact geometry of the problem and to reduce or cancel mesh generation time by using NURBS curves employed in computer aided designs as a tool for isogeometric analysis. The present formulation extends such curves to be implemented as a stress analysis tool.

Sign in / Sign up

Export Citation Format

Share Document