Best theory diagram for metallic and laminated composite plates

The objective of this article is to present an investigation on the various theories and presented some classical and high order models, these models to use the new function f(z) for the static and dynamic analysis of plates (laminate, Composite and FGM) as well as those theories which have been developed in the literature to improve the evolution of the variation of the field of displacements in the thickness of the materials.

AIAA Journal, 2010

2012

The paper summerises some basic trends in modelling and analysis of refined plate theories not primary from a mathematical aspect but from the viewpoint of engineering application and of an increasing reliability of engineering structure analysis. Shear rigid and shear deformable plate models including shear correction factors or kinematical warping effects can be formulated. An extended two-dimensional theory for transverse shear stress analysis yields improved results, the influence of singularities on the global structure behaviour must be considered and the kinematical degree of freedom of plate models is an important criterion in structural analysis of folded plate structures. Composite materials have become an increasing importance in engineering structures. Multilayered, laminated and sandwich plates are used in aerospace and many other industries. Thin-walled structures composed of composite material have generally a moderate thickness and low transverse stiffness. An adequa...

Plate Analysis Numerical and Engineering Methods, 2014

Theories and Applications of Plate Analysis Classical, Numerical and Engineering Methods Rudolph Szilard, Dr.-Ing., P.E. Professor Emeritus of Structural Mechanics University of Hawaii, United States Retired Chairman, Department of Structural Mechanics University of Dortmund, Germany

European Journal of Mechanics - A/Solids

In structural analysis, many components are approximated as plates. More often that not, classical plate theories, such as Kirchhoff or Reissner-Mindlin plate theories, form the basis of the analytical developments. The advantage of these approaches is that they leads to simple kinematic descriptions of the problem: the plate's normal material line is assumed to remain straight and its displacement field is fully defined by three displacement and two rotation components. While such approach is capable of capturing the kinetic energy of the system accurately, it cannot represent the strain energy adequately. For instance, it is well known from three-dimensional elasticity theory that the normal material line will warp under load for laminated composite plates, leading to three-dimensional deformations that generate complex stress states. To overcome this problem, several layer-wise plate theories have been proposed. While these approaches work well for some cases, they often lead to inefficient formulations because they introduce numerous additional variables. This paper presents a novel, single-layer theory using local-global Approach: based on a finite element semi-discretization of the normal material line, the two-dimensional plate equations are derived from three-dimensional elasticity using a rigorous dimensional reduction procedure. Three-dimensional stresses through the plate's thickness can be recovered accurately from the plate's stress resultants.

AIAA Journal, 1998

The evaluation of mixed layerwise theories to calculate the in-plane and out-of-plane responses of thick plates in two-dimensional modeling of multilayered structures is made. The employed models, which were proposed by the author in earlier works, a priori fulfill the continuity of transverse shear and normal stress components at the interface between two adjacent layers. A Reissner's mixed variational equation is used to derive the governing equations, in terms of introduced stress and displacement variables. The interface continuity conditions are imposed by writing the governing equations at a multilayered level. The related standard displacement formulations are also discussed for comparison purpose. Closed-form solutions are presented for plates made of orthotropic lamina and bent by harmonic distribution of transverse pressure. Symmetrically and unsymmetrically laminated, as well as sandwich, plates have been investigated. A comparison with a three-dimensional-elasticity analysis shows that present mixed layerwise models furnish a better description of the in-plane and out-of-plane response of thick plates with respect to existing layerwise and equivalent single-layer theories. In particular, the proposed models describe, with excellent accuracy, the transverse shear and normal stress fields. Unlike available current models, these fields are herein determined a priori without requiring implementation of any postprocessing procedures. The distribution of the transverse displacement and transverse normal stress in the plate thickness direction are also shown for most of the problems.

Facta universitatis - series: Architecture and Civil Engineering, 2005

This paper deals with closed-form solution for static analysis of simply supported composite plate, based on generalized laminate plate theory (GLPT). The mathematical model assumes piece-wise linear variation of in-plane displacement components and a constant transverse displacement through the thickness. It also include discrete transverse shear effect into the assumed displacement field, thus providing accurate prediction of transverse shear stresses. Namely, transverse stresses satisfy Hook's law, 3D equilibrium equations and traction free boundary conditions. With assumed displacement field, linear strain-displacement relation, and constitutive equations of the lamina, equilibrium equations are derived using principle of virtual displacements. Navier-type closed form solution of GLPT, is derived for simply supported plate, made of orthotropic laminae, loaded by harmonic and uniform distribution of transverse pressure. Results are compared with 3D elasticity solutions and excellent agreement is found.

1996