Large Deflection Geometrically Nonlinear Behaviour of Laterally Loaded Segmental Plates

2009 ◽  
Author(s):  
A.B. Sabir ◽  
H.G.V. Avanessian
Keyword(s):  
Large Deflection ◽  
Nonlinear Behaviour ◽  
Geometrically Nonlinear ◽  
Laterally Loaded

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.

Approximate Structural Analysis of Circuit Card Systems Subjected to Torsion

1992 ◽  
Vol 114 (2) ◽  
pp. 203-210 ◽  
Author(s):  
P. A. Engel ◽  
J. T. Vogelmann
Keyword(s):  
Finite Element ◽  
Structural Analysis ◽  
Large Deflection ◽  
Torsional Stiffness ◽  
Geometrically Nonlinear ◽  
Engineering Analysis ◽  
Printed Circuit ◽  
Engineering Theory ◽  
Simplified Method ◽  
Numerical Finite Element

Engineering analysis of module-populated printed circuit cards subjected to torsion is pursued by approximate engineering analysis, numerical (finite element), and experimental means. The engineering theory utilizes a simplified method of evaluating the torsional stiffness and maximum lead force, the latter found at the module corners. Finite element methods are used to check these values for circuit cards with a wide variety of module configurations, starting from a single-module to sixteen PLCC modules, having 44, 68, and 84 J-leads. An experimental torsion apparatus is used to obtain data for further comparison with the former approaches, and for getting data from the geometrically nonlinear (large deflection) range.

scholarly journals Axisymmetric Large Deflection Elastic Analysis of Hollow Annular Membranes under Transverse Uniform Loading

Symmetry ◽  
2021 ◽  
Vol 13 (10) ◽  
pp. 1770
Author(s):  
Jun-Yi Sun ◽  
Qi Zhang ◽  
Xue Li ◽  
Xiao-Ting He
Keyword(s):  
Closed Form ◽  
Circular Plate ◽  
Large Deflection ◽  
Closed Form Solution ◽  
Circular Ring ◽  
Form Solution ◽  
Elastic Response ◽  
Geometrically Nonlinear ◽  
Closed Form Solutions ◽  
Annular Membrane

The anticipated use of a hollow linearly elastic annular membrane for designing elastic shells has provided an impetus for this paper to investigate the large deflection geometrically nonlinear phenomena of such a hollow linearly elastic annular membrane under transverse uniform loads. The so-called hollow annular membranes differ from the traditional annular membranes available in the literature only in that the former has the inner edge attached to a movable but weightless rigid concentric circular ring while the latter has the inner edge attached to a movable but weightless rigid concentric circular plate. The hollow annular membranes remove the transverse uniform loads distributed on “circular plate” due to the use of “circular ring” and result in a reduction in elastic response. In this paper, the large deflection geometrically nonlinear problem of an initially flat, peripherally fixed, linearly elastic, transversely uniformly loaded hollow annular membrane is formulated, the problem formulated is solved by using power series method, and its closed-form solution is presented for the first time. The convergence and effectiveness of the closed-form solution presented are investigated numerically. A comparison between closed-form solutions for hollow and traditional annular membranes under the same conditions is conducted, to reveal the difference in elastic response, as well as the influence of different closed-form solutions on the anticipated use for designing elastic shells.

Nonlinear Behaviour of Unsymmetric, Angle-Ply, Rectangular Plates under in-Plane Edge Shear

1979 ◽  
Vol 21 (3) ◽  
pp. 205-212 ◽  
Author(s):  
M. K. Prabhakara ◽  
J. B. Kennedy
Keyword(s):  
Large Deflection ◽  
Bending Moment ◽  
Double Series ◽  
Nonlinear Behaviour ◽  
Rectangular Plates ◽  
Bending Moments ◽  
High Modulus ◽  
Buckling Loads ◽  
Post Buckling ◽  
Transverse Deflection

A nonlinear analysis of unsymmetric, angle-ply, rectangular plates under uniform in-plane edge shear is presented. The solution is based on the von Kármán-type large-deflection equations, with the force function and the transverse deflection expressed as double series in terms of appropriate beam functions. The prescribed boundary conditions, including those for the vanishing of normal bending moment at the edges of simply supported plates, are satisfied. Numerical results for the buckling loads and for the post-buckling deflections, membrane forces and bending moments are presented for plates composed of high-modulus, fibre-reinforced epoxy composites.

scholarly journals Self-moments stiffening effect and buckling strength of periodic Vierendeel beams

2020 ◽  
Author(s):  
Francesco Penta
Keyword(s):  
Closed Form ◽  
Large Deflection ◽  
Continuous System ◽  
Equivalent Model ◽  
Geometrically Nonlinear ◽  
Closed Form Solutions ◽  
Expansion Technique ◽  
Polar Model ◽  
The Galerkin Method ◽  
Stiffening Effect

AbstractThis paper deals with the buckling phenomenon of periodic Vierendeel beams. Closed-form solutions for critical loads and deformed shapes are presented. They are built by exploiting several auxiliary solutions obtained for the discrete periodic girder and for a geometrically nonlinear micro-polar equivalent model. In particular, the girder when subjected to sinusoidal self-equilibrated systems of inner bending moments (self-moments) is analysed. The corresponding results are used for solving the large-deflection equilibrium problem of the continuous equivalent model by means of the eigenfunction expansion technique. Girder buckling conditions are then defined in terms of kinematics of the micro-polar model: more precisely, they are attained when special distributions of self-moments, able to bend the continuous system without violating compatibility of shear strains, act in the girder. It is shown that these systems, neglected in the theories presented so far, have a significant stiffening effect on the buckling girder behaviour. Moreover, they are governed by the continuity equation for micro-rotations that is solved in closed form by the Galerkin method, with the micro-polar model eigenfunctions as basis functions. The accuracy of the proposed solutions is verified by comparing them with those achieved by a series of finite element girder models.

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