Stress analysis in transverse loading of soft core sandwich plates with various boundary conditions

2018 ◽  
Vol 22 (8) ◽  
pp. 2692-2734 ◽  
Author(s):  
Isa Ahmadi
Keyword(s):  
Boundary Conditions ◽  
Three Dimensional ◽  
Stress Singularity ◽  
Sandwich Plates ◽  
Local Concentration ◽  
Governing Equations ◽  
Transverse Loading ◽  
Weak Formulation ◽  
Various Boundary Conditions ◽  
Out Of Plane

In this paper, the transverse loading of sandwich plate is formulated to study the three-dimensional stress field in the sandwich plates for various edge conditions. The formulation is based on the weak formulation approach. A complete three-dimensional displacement field is considered and the weak formulation approach is employed to obtain the governing equations of the plate using the three dimensional equilibrium equations of elasticity. An analytical solution is presented for governing equations when two opposite edges of plate are simply supported. A one-step stress recovery scheme is used to compute the out-of-plane stresses in the sandwich plates. A comparison is made with the predictions of exact elasticity solutions in the open literature and very good agreements are achieved. The distribution of stresses is investigated for various boundary conditions and the log-linear procedure is employed to study the order of stress singularity at free and clamped edge of the plate. It is seen that the present approach accurately predicts the distribution of out-of-plane stresses and local concentration of stresses in the vicinity of free and clamped edges of sandwich structures.

A refined quasi-3D shear deformation theory for thermo-mechanical behavior of functionally graded sandwich plates on elastic foundations

2017 ◽  
Vol 21 (6) ◽  
pp. 1906-1929 ◽  
Author(s):  
Abdelkader Mahmoudi ◽  
Samir Benyoucef ◽  
Abdelouahed Tounsi ◽  
Abdelkader Benachour ◽  
El Abbas Adda Bedia ◽  
...  
Keyword(s):  
Boundary Conditions ◽  
Shear Deformation ◽  
Elastic Foundation ◽  
Deformation Theory ◽  
Three Dimensional ◽  
Shear Deformation Theory ◽  
Functionally Graded ◽  
Sandwich Plates ◽  
Refined Theory ◽  
Governing Equations

In this paper, a refined quasi-three-dimensional shear deformation theory for thermo-mechanical analysis of functionally graded sandwich plates resting on a two-parameter (Pasternak model) elastic foundation is developed. Unlike the other higher-order theories the number of unknowns and governing equations of the present theory is only four against six or more unknown displacement functions used in the corresponding ones. Furthermore, this theory takes into account the stretching effect due to its quasi-three-dimensional nature. The boundary conditions in the top and bottoms surfaces of the sandwich functionally graded plate are satisfied and no correction factor is required. Various types of functionally graded material sandwich plates are considered. The governing equations and boundary conditions are derived using the principle of virtual displacements. Numerical examples, selected from the literature, are illustrated. A good agreement is obtained between numerical results of the refined theory and the reference solutions. A parametric study is presented to examine the effect of the material gradation and elastic foundation on the deflections and stresses of functionally graded sandwich plate resting on elastic foundation subjected to thermo-mechanical loading.

Plane-Stress Deformation in Strain Gradient Plasticity

1999 ◽  
Vol 67 (1) ◽  
pp. 105-111 ◽  
Author(s):  
J. Y. Chen ◽  
Y. Huang ◽  
K. C. Hwang ◽  
Z. C. Xia
Keyword(s):  
Boundary Conditions ◽  
Plane Stress ◽  
Strain Gradient ◽  
Three Dimensional ◽  
Strain Gradient Plasticity ◽  
Plane Boundary ◽  
Gradient Plasticity ◽  
Governing Equations ◽  
Stress Deformation ◽  
Out Of Plane

A systematic approach is proposed to derive the governing equations and boundary conditions for strain gradient plasticity in plane-stress deformation. The displacements, strains, stresses, strain gradients and higher-order stresses in three-dimensional strain gradient plasticity are expanded into a power series of the thickness h in the out-of-plane direction. The governing equations and boundary conditions for plane stress are obtained by taking the limit h→0. It is shown that, unlike in classical plasticity theories, the in-plane boundary conditions and even the order of governing equations for plane stress are quite different from those for plane strain. The kinematic relations, constitutive laws, equilibrium equation, and boundary conditions for plane-stress strain gradient plasticity are summarized in the paper. [S0021-8936(00)02301-1]

Application of Generalized Differential Quadrature Method to the Bending of Thick Laminated Plates with Various Boundary Conditions

2006 ◽  
Vol 5-6 ◽  
pp. 407-414 ◽  
Author(s):  
Mohammad Mohammadi Aghdam ◽  
M.R.N. Farahani ◽  
M. Dashty ◽  
S.M. Rezaei Niya
Keyword(s):  
Boundary Condition ◽  
Boundary Conditions ◽  
Simple Procedure ◽  
Shear Deformation Theory ◽  
Laminated Plates ◽  
Differential Quadrature ◽  
Governing Equations ◽  
First Order ◽  
Various Boundary Conditions ◽  
Generalized Differential

Bending analysis of thick laminated rectangular plates with various boundary conditions is presented using Generalized Differential Quadrature (GDQ) method. Based on the Reissner first order shear deformation theory, the governing equations include a system of eight first order partial differential equations in terms of unknown displacements, forces and moments. Presence of all plate variables in the governing equations provide a simple procedure to satisfy different boundary condition during application of GDQ method to obtain accurate results with relatively small number of grid points even for plates with free edges .Illustrative examples including various combinations of clamped, simply supported and free boundary condition are given to demonstrate the accuracy and convergence of the presented GDQ technique. Results are compared with other analytical and finite element predictions and show reasonably good agreement.

Investigation of heat transfer in irregular porous cavity subjected to various boundary conditions

2019 ◽  
Vol 29 (1) ◽  
pp. 418-447 ◽  
Author(s):  
Irfan Anjum Badruddin
Keyword(s):  
Heat Transfer ◽  
Boundary Conditions ◽  
Outer Boundary ◽  
Governing Equations ◽  
Content Type ◽  
Porous Cavity ◽  
Various Boundary Conditions ◽  
Heating Source ◽  
Transfer Behavior ◽  
Vertical Walls

Purpose The purpose of this paper is to investigate the heat transfer in an arbitrary cavity filled with porous medium. The geometry of the cavity is such that an isothermal heating source is placed centrally at the bottom of the cavity. The height and width of the heating source is varied to analyses its effect on the heat transfer characteristics. The investigation is carried out for three different cases of outer boundary conditions such as two outside vertical walls being maintained at cold temperature To, two vertical and top horizontal surface being heated to. To and the third case with top surface kept at To but other surfaces being adiabatic. Design/methodology/approach Finite element method is used to solve the governing equations. Findings It is observed that the cavity exhibits unique heat transfer behavior as compared to regular cavity. The cases of boundary conditions are found to affect the heat transfer rate in the porous cavity. Originality/value This is original work representing the heat transfer in irregular porous cavity with various boundary conditions. This work is neither being published nor under review in any other journal.

Lateral Buckling of Cantilevered Circular Arches Under Various End Moments

2020 ◽  
Vol 20 (07) ◽  
pp. 2071005
Author(s):  
Y. B. Yang ◽  
Y. Z. Liu
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Analytical Solutions ◽  
Analytical Approach ◽  
Three Dimensional ◽  
Curved Beams ◽  
Lateral Buckling ◽  
Circular Arch ◽  
Out Of Plane ◽  
The Moment

Lateral buckling of cantilevered circular arches under various end moments is studied using an analytical approach. Three types of conservative moments are considered, i.e. the quasi-tangential moments of the 1st and 2nd kinds, and the semi-tangential moment. The induced moments associated with each of the moment mechanisms undergoing three-dimensional rotations are included in the Newman boundary conditions. Using the differential equations available for the out-of-plane buckling of curved beams, the analytical solutions are derived for a cantilevered circular arch, which can be used as the benchmarks for calibration of other methods of analysis.

A Node-Dependent Kinematic Approach for Rotordynamics Problems

2019 ◽  
Vol 141 (6) ◽  
Author(s):  
Matteo Filippi ◽  
Enrico Zappino ◽  
Erasmo Carrera
Keyword(s):  
Dynamic Analysis ◽  
Computational Cost ◽  
Three Dimensional ◽  
Governing Equations ◽  
Three Dimensional Model ◽  
Flexible Supports ◽  
Out Of Plane ◽  
Kinematic Models ◽  
Carrera Unified Formulation ◽  
Kinematic Approach

This paper presents the dynamic analysis of rotating structures using node-dependent kinematics (NDK) one-dimensional (1D) elements. These elements have the capabilities to assume a different kinematic at each node of a beam element, that is, the kinematic assumptions can be continuously varied along the beam axis. Node-dependent kinematic 1D elements have been extended to the dynamic analysis of rotors where the response of the slender shaft, as well as the responses of disks, has to be evaluated. Node dependent kinematic capabilities have been exploited to impose simple kinematic assumptions along the shaft and refined kinematic models where the in- and out-of-plane deformations appear, that is, on the disks. The governing equations of the rotordynamics problem have been derived in a unified and compact form using the Carrera unified formulation. Refined beam models based on Taylor and Lagrange expansions (LEs) have been considered. Single- and multiple-disk rotors have been investigated. The effects of flexible supports have also been included. The results show that the use of the node-dependent kinematic elements allows the accuracy of the model to be increased only where it is required. This approach leads to a reduction of the computational cost compared to a three-dimensional model while the accuracy of the results is preserved.

scholarly journals Aspects of Computational Homogenization at Finite Deformations: A Unifying Review From Reuss' to Voigt's Bound

2016 ◽  
Vol 68 (5) ◽  
Author(s):  
Saba Saeb ◽  
Paul Steinmann ◽  
Ali Javili
Keyword(s):  
Finite Element ◽  
Boundary Conditions ◽  
Three Dimensional ◽  
Linear Displacement ◽  
Computational Homogenization ◽  
Finite Strains ◽  
Underlying Assumption ◽  
Numerical Examples ◽  
Various Boundary Conditions ◽  
Computational Aspects

The objective of this contribution is to present a unifying review on strain-driven computational homogenization at finite strains, thereby elaborating on computational aspects of the finite element method. The underlying assumption of computational homogenization is separation of length scales, and hence, computing the material response at the macroscopic scale from averaging the microscopic behavior. In doing so, the energetic equivalence between the two scales, the Hill–Mandel condition, is guaranteed via imposing proper boundary conditions such as linear displacement, periodic displacement and antiperiodic traction, and constant traction boundary conditions. Focus is given on the finite element implementation of these boundary conditions and their influence on the overall response of the material. Computational frameworks for all canonical boundary conditions are briefly formulated in order to demonstrate similarities and differences among the various boundary conditions. Furthermore, we detail on the computational aspects of the classical Reuss' and Voigt's bounds and their extensions to finite strains. A concise and clear formulation for computing the macroscopic tangent necessary for FE2 calculations is presented. The performances of the proposed schemes are illustrated via a series of two- and three-dimensional numerical examples. The numerical examples provide enough details to serve as benchmarks.

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