The Experts below are selected from a list of 312 Experts worldwide ranked by ideXlab platform
G. Shi - One of the best experts on this subject based on the ideXlab platform.
-
A refined laminated Plate Theory accounting for the third-order shear deformation and interlaminar transverse stress continuity
Applied Mathematical Modelling, 2015Co-Authors: X. Wang, G. ShiAbstract:Abstract A variational consistent third-order shear laminated Plate Theory accounting for the transverse shear stress continuity at the interlaminar interfaces of laminated Plates is developed in this paper. The transverse shear function used in this new laminated Plate Theory is based on the kinematics in the third-order shear deformation Plate Theory proposed by Shi (2007). The variational principle is employed to derive the variational consistent equilibrium equations in terms of displacements and the variational boundary conditions in terms of displacements and equivalent stress resultants. The continuity conditions of the in-plane displacements and transverse shear stresses at the interlaminar interfaces of laminated Plates are enforced by the Heaviside step functions and continuity coefficients. The resulting new laminated composite Plate Theory accounting for interlaminar continuity has only five independent field variables. Furthermore, the number of the field variables in the present third-order shear laminated Plate Theory is the same as that used in the first-order shear deformation Plate Theory. The refined laminated Plate Theory is applied to solve the bending problems of four laminated composite Plates with different lamination schemes and different aspect ratios to evaluate its reliability and accuracy. The resulting analytical solutions of both deflections and stresses agree well with the 3D elasticity solutions and the numerical results of finite element analysis. The result comparison with other laminated Plate theories shows that new laminated Plate Theory accounting for the interlaminar continuity proposed in this paper yields more accurate displacements and stresses than other laminated Plate theories with five global variables. Because only five field variables are used in this new laminated Plate Theory with interlaminar continuity, this refined laminated Plate Theory can be used as an accurate and efficient theoretical model for the finite element analysis of laminated composite Plates.
-
A simple and accurate sandwich Plate Theory accounting for transverse normal strain and interfacial stress continuity
Composite Structures, 2014Co-Authors: X. Wang, G. ShiAbstract:Abstract This paper presents a simple and accurate sandwich Plate Theory accounting for the transverse normal strain and interfacial stress continuity. A refined cubic polynomial is used for the transverse shear function and a linear function is adopted for the transverse normal strain. The Heaviside step function and stress continuity coefficients are employed respectively to enforce the interfacial continuity of the in-plane displacements and transverse stresses. By the enforcement of the traction conditions on the Plate surfaces, there are only five independent field variables in the present sandwich Plate Theory. The variational consistent equilibrium equations and boundary conditions in terms of both displacements and stress resultants are derived by utilizing the variational principle. The analytical solutions of the bending analyses of sandwich Plates with different aspect ratios and stiffness ratios are solved to demonstrate the accuracy of this new sandwich Plate Theory. The resulting analytical solutions of deflections, normal stresses and transverse shear stresses are compared with the 3D elasticity solutions, the numerical results and the results given by other sandwich Plate theories. The comparison study shows that this equivalent single layer sandwich Plate Theory is not only simple, but also capable of achieving the accuracy of layerwise sandwich Plate theories.
X. Wang - One of the best experts on this subject based on the ideXlab platform.
-
A refined laminated Plate Theory accounting for the third-order shear deformation and interlaminar transverse stress continuity
Applied Mathematical Modelling, 2015Co-Authors: X. Wang, G. ShiAbstract:Abstract A variational consistent third-order shear laminated Plate Theory accounting for the transverse shear stress continuity at the interlaminar interfaces of laminated Plates is developed in this paper. The transverse shear function used in this new laminated Plate Theory is based on the kinematics in the third-order shear deformation Plate Theory proposed by Shi (2007). The variational principle is employed to derive the variational consistent equilibrium equations in terms of displacements and the variational boundary conditions in terms of displacements and equivalent stress resultants. The continuity conditions of the in-plane displacements and transverse shear stresses at the interlaminar interfaces of laminated Plates are enforced by the Heaviside step functions and continuity coefficients. The resulting new laminated composite Plate Theory accounting for interlaminar continuity has only five independent field variables. Furthermore, the number of the field variables in the present third-order shear laminated Plate Theory is the same as that used in the first-order shear deformation Plate Theory. The refined laminated Plate Theory is applied to solve the bending problems of four laminated composite Plates with different lamination schemes and different aspect ratios to evaluate its reliability and accuracy. The resulting analytical solutions of both deflections and stresses agree well with the 3D elasticity solutions and the numerical results of finite element analysis. The result comparison with other laminated Plate theories shows that new laminated Plate Theory accounting for the interlaminar continuity proposed in this paper yields more accurate displacements and stresses than other laminated Plate theories with five global variables. Because only five field variables are used in this new laminated Plate Theory with interlaminar continuity, this refined laminated Plate Theory can be used as an accurate and efficient theoretical model for the finite element analysis of laminated composite Plates.
-
A simple and accurate sandwich Plate Theory accounting for transverse normal strain and interfacial stress continuity
Composite Structures, 2014Co-Authors: X. Wang, G. ShiAbstract:Abstract This paper presents a simple and accurate sandwich Plate Theory accounting for the transverse normal strain and interfacial stress continuity. A refined cubic polynomial is used for the transverse shear function and a linear function is adopted for the transverse normal strain. The Heaviside step function and stress continuity coefficients are employed respectively to enforce the interfacial continuity of the in-plane displacements and transverse stresses. By the enforcement of the traction conditions on the Plate surfaces, there are only five independent field variables in the present sandwich Plate Theory. The variational consistent equilibrium equations and boundary conditions in terms of both displacements and stress resultants are derived by utilizing the variational principle. The analytical solutions of the bending analyses of sandwich Plates with different aspect ratios and stiffness ratios are solved to demonstrate the accuracy of this new sandwich Plate Theory. The resulting analytical solutions of deflections, normal stresses and transverse shear stresses are compared with the 3D elasticity solutions, the numerical results and the results given by other sandwich Plate theories. The comparison study shows that this equivalent single layer sandwich Plate Theory is not only simple, but also capable of achieving the accuracy of layerwise sandwich Plate theories.
Hui-hui Dai - One of the best experts on this subject based on the ideXlab platform.
-
On a uniformly-valid asymptotic Plate Theory
International Journal of Non-Linear Mechanics, 2019Co-Authors: Fan-fan Wang, David J. Steigmann, Hui-hui DaiAbstract:Abstract A uniformly-valid Plate Theory, independent of the magnitudes of applied loads, is derived based on the two-dimensional Plate Theory obtained from series expansions about the bottom surface of a Plate. For five different magnitudes of surface loads, it is shown by using asymptotic expansions that this unified Plate Theory recovers five well-known Plate models in the literature to leading-order. This demonstrates its uniform validity. More generally, it provides a uniformly-valid Plate model provided that two asymptotic conditions are satisfied, which can be checked as a posteriori. The weak formulation of the uniformly-valid Plate equations is furnished, which can be used for finite element implementation.
-
An incremental Plate Theory for polymer gels in equilibrium
Mechanics Research Communications, 2019Co-Authors: Xiaoyi Chen, Hui-hui DaiAbstract:Abstract Based on the finite-strain Plate Theory derived by one of the authors, an incremental Plate Theory for deformations superimposed on a general base state is formulated in this paper. The unknown functions of the incremental deformation are first expanded into Taylor series in terms of the thickness variable and then expanded around the base state by retaining third-order nonlinearity. From the field equations and the boundary conditions at the top and bottom surfaces, the recursive relations of the expansion coefficients as well as the incremental balance equations are derived. With the constitutive relation for swollen polymer gels in equilibrium, an incremental Plate Theory is obtained. As an application, this Theory is used to study the incremental deformation of a polymer gel layer with a homogeneous base state in a plane strain setting. A linear bifurcation analysis is carried out, which gives the critical values of the external chemical potential and the mode number. The results agree with those obtained directly from a full two-dimensional analysis. Post-bifurcation is also conducted through a perturbation procedure, which reveals that the bifurcation is of supercritical type.
-
on a consistent finite strain Plate Theory of growth
Journal of The Mechanics and Physics of Solids, 2018Co-Authors: Jiong Wang, Fan-fan Wang, David J. Steigmann, Hui-hui DaiAbstract:Abstract In this paper, a consistent finite-strain Plate Theory for growth-induced large deformations is developed. The three-dimensional (3D) governing system of the Plate model is formulated through the variational approach, which is composed of the mechanical equilibrium equation and the constraint equation of incompressibility. Then, series expansions of the unknown functions in terms of the thickness variable are adopted. By using the 3D equilibrium equations and the surface boundary conditions, recursion relations for the expansion coefficients are successfully established. As a result, a 2D vector Plate equation with three unknowns is obtained and the associated edge boundary conditions are proposed. It can be verified that the Plate equation ensures the required asymptotic order for all the terms in the variations of the total energy functional. The weak formulation of the Plate equation has also been derived for future numerical calculations. As applications of the Plate Theory, two examples regarding the growth-induced deformations and instabilities in thin hyperelastic Plates are studied. Some analytical results are obtained in these examples, which can be used to describe the large deformations and reveal the bifurcation properties of the thin Plates. Furthermore, the results obtained from the current Plate Theory are compared with those obtained from the classical Foppl-von Karman Plate Theory, from which the efficiencies and advantages of the current Plate Theory can be demonstrated.
-
on a consistent finite strain Plate Theory for incompressible hyperelastic materials
International Journal of Solids and Structures, 2016Co-Authors: Jiong Wang, Zilong Song, Hui-hui DaiAbstract:Abstract In this paper, a consistent finite-strain Plate Theory for incompressible hyperelastic materials is formulated. Within the framework of nonlinear elasticity and through a variational approach, the three-dimensional (3D) governing system is derived. Series expansions of the independent variables in the governing system are taken about the bottom surface of the Plate, which, together with some further manipulations, yield a 2D vector Plate equation. Suitable position and traction boundary conditions on the edge are also proposed. The 2D Plate system ensures that each term in the variations of the generalized potential energy functional attains the required asymptotic order. The associated weak formulation of the Plate model is also derived, and can be simplified to accommodate distinct types of practical edge conditions. To demonstrate the validity of the derived 2D vector Plate system, the pure finite-bending of a Plate made of an incompressible neo-Hookean material is studied. Both the exact solutions and the Plate solutions of the problem are obtained. Through some comparisons, it is found that the Plate Theory can provide second-order correct results.
-
on a consistent finite strain Plate Theory based on three dimensional energy principle
Proceedings of The Royal Society A: Mathematical Physical and Engineering Sciences, 2014Co-Authors: Hui-hui Dai, Zilong SongAbstract:This paper derives a finite-strain Plate Theory consistent with the principle of stationary three-dimensional potential energy under general loadings with a fourth-order error. Starting from the three-dimensional nonlinear elasticity (with both geometrical and material nonlinearity) and by a series expansion, we deduce a vector Plate equation with three unknowns, which exhibits the local force-balance structure. The success relies on using the three-dimensional field equations and bottom traction condition to derive exact recursion relations for the coefficients. Associated weak formulations are considered, leading to a two-dimensional virtual work principle. An alternative approach based on a two-dimensional truncated energy is also provided, which is less consistent than the first Plate Theory but has the advantage of the existence of a two-dimensional energy function. As an example, we consider the pure bending problem of a hyperelastic block. The comparison between the analytical Plate solution and available exact one shows that the Plate Theory gives second-order correct results. Compared with existing Plate theories, it appears that the present one has a number of advantages, including the consistency, order of correctness, generality of loadings, applicability to finite-strain problems and no involvement of non-physical quantities.
Anthony N Palazotto - One of the best experts on this subject based on the ideXlab platform.
-
A higher-order sandwich Plate Theory accounting for 3-D stresses
International Journal of Solids and Structures, 2001Co-Authors: Anthony N PalazottoAbstract:In this paper we extend a layerwise higher-order shear-deformation Theory to model a sandwich Plate impacting with an elastic foundation at a low velocity. A new concept of sublaminates is introduced, and the new sandwich Plate Theory satisfies the continuity conditions of interlaminar shear and normal stresses, accommodates the normal and shear stresses on the bonding surfaces, and accounts for non-uniform distributions of transverse shear stresses in each layer. Moreover, the use of sublaminates enables the modeling of shear warpings that change with the spatial location, vibration frequency, and loading and boundary conditions. A finite-element model based on this sandwich Plate Theory is derived for performing direct transient analyses to predict the initiation and location of critical matrix crack and the threshold of impact damage. Moreover, analytical shear warping functions, shear coupling functions, and normal strain functions due to in-plane stretching, bending, transverse shearing, and surface loading are presented.
C M Wang - One of the best experts on this subject based on the ideXlab platform.
-
exact solutions for axisymmetric bending of micro nanoscale circular Plates based on nonlocal Plate Theory
Nanotechnology, 2007Co-Authors: Wenhui Duan, C M WangAbstract:Axisymmetric bending of micro/nanoscale circular Plates is studied using a nonlocal Plate Theory. The nonlocal Theory allows for small scale effects. The governing equations and boundary conditions are derived for the aforementioned problem. By using a variable transformation technique, exact nonlocal solutions for axisymmetric bending of circular Plates under general loading are obtained. A detailed examination of the effects of small scale on nonlocal solutions is carried out using uniformly loaded circular Plates with either clamped or simply-supported edges. When compared with local Plate Theory, the nonlocal solutions show larger deflections, moments and shear force and lower bending stiffness.
-
bending solutions of sectorial thick Plates based on reissner Plate Theory
Mechanics Based Design of Structures and Machines, 2005Co-Authors: C M Wang, I M Nazmul, Takashi Matsumoto, Q WangAbstract:This paper is concerned with the bending of sectorial and annular sectorial thick Plates with the radial edges simply supported. The Reissner Plate Theory has been adopted to cater for the effect of transverse shear deformation. In solving the aforementioned Plate problems, we derive the relationships between the bending solutions of the Reissner Plate Theory and the classical thin Plate Theory. The relationships enable one to deduce the bending solutions of the Reissner Plate Theory using the corresponding classical thin Plate results, which can be determined readily or are already available in the literature. Several sectorial Plate problems are solved, and the Reissner Plate results are checked against existing numerical results as well as results obtained using other higher-order Plate theories.
-
Buckling of circular Plates based on Reddy Plate Theory
ASME 1997 Turbo Asia Conference, 1997Co-Authors: C M Wang, K H Lee, J N ReddyAbstract:Treated herein is the elastic buckling of circular Plates based on the Reddy Plate Theory. This Plate Theory extends the Kirchhoff (or the classical thin) Plate Theory to allow for the effect of transverse shear deformation. Unlike the Mindlin's shear deformation Plate Theory, there is no need for a shear correction factor in the Reddy Plate Theory. In this paper, exact buckling solutions are derived for circular Plates whose edges are simply supported and elastically restrained against rotation as well. This general edge condition includes the classical simply supported and clamped edges at the limiting, values of the elastic rotational restraint constant. The buckling solutions are expressed in terms of the well-known Kichhoff buckling solutions. A comparison of buckling loads between the Mindlin, Reddy and three-dimensional elasticity Plates is also given.