Thermoelastic Fields in Boundary Layers of Isotropic Laminates

2005 ◽  
Vol 72 (1) ◽  
pp. 86-101 ◽  
Author(s):  
Christian Mittelstedt ◽  
Wilfried Becker
Keyword(s):  
Closed Form ◽  
Edge Effects ◽  
Plate Theory ◽  
Closed Form Solution ◽  
Laminate Plate ◽  
Free Edge ◽  
Linear Displacement ◽  
Form Solution ◽  
State Variables ◽  
Layered Plates

An approximate approach to the calculation of displacements, strains, and stresses near edges and corners in symmetric rectangular layered plates of dissimilar isotropic materials under thermal load is presented. In the thickness direction the plate is discretized into an arbitrary number of sublayers/mathematical layers. A layerwise linear displacement field is formulated such that the terms according to classical laminate plate theory are upgraded with unknown in-plane functions and a linear interpolation scheme through the layer thickness in order to describe edge and corner perturbations. By virtue of the principle of minimum potential energy the governing coupled Euler–Lagrange differential equations are derived, which in the case of free-edge effects allow a closed-form solution for the unknown inplane functions. Free-corner effects are investigated by combining the displacement formulations of the two interacting free-edge effects. Hence, all state variables in the plate are obtained in a closed-form manner. Boundary conditions of traction free plate edges are satisfied in an integral sense. The present methodology is easily applied and requires only reasonable computational expenses.

A closed form solution for bending/stretching analysis of functionally graded circular plates under asymmetric loading using the Green function

2010 ◽  
Vol 224 (6) ◽  
pp. 1153-1163 ◽  
Author(s):  
A R Saidi ◽  
A Naderi ◽  
E Jomehzadeh
Keyword(s):  
Green Function ◽  
Closed Form ◽  
Volume Fraction ◽  
Plate Theory ◽  
Closed Form Solution ◽  
Form Solution ◽  
Functionally Graded ◽  
Transverse Displacement ◽  
Circular Plates ◽  
Equilibrium Equations

In this article, a closed-form solution for bending/stretching analysis of functionally graded (FG) circular plates under asymmetric loads is presented. It is assumed that the material properties of the FG plate are described by a power function of the thickness variable. The equilibrium equations are derived according to the classical plate theory using the principle of total potential energy. Two new functions are introduced to decouple the governing equilibrium equations. The three highly coupled partial differential equations are then converted into an independent equation in terms of transverse displacement. A closed-form solution for deflection of FG circular plates under arbitrary lateral eccentric concentrated force is obtained by defining a new coordinate system. This solution can be used as a Green function to obtain the closed-form solution of the FG plate under arbitrary loadings. Also, the solution is employed to solve some different asymmetric problems. Finally, the stress and displacement components are obtained exactly for each problem and the effect of volume fraction is also studied.

Flexural stiffness of leaf springs for compliant micromechanisms

2008 ◽  
Vol 222 (12) ◽  
pp. 2505-2511 ◽  
Author(s):  
P Angeli ◽  
F De Bona ◽  
M G Munteanu
Keyword(s):  
Closed Form ◽  
Plate Theory ◽  
Closed Form Solution ◽  
Form Solution ◽  
Constant Thickness ◽  
Flexural Stiffness ◽  
Beam Model ◽  
Flexural Behaviour ◽  
Leaf Springs ◽  
Linear Behaviour

Von Kármán equations have been used to evaluate the flexural behaviour of rectangular leaf springs with constant thickness. A closed form solution is obtained, showing that flexural stiffness varies continuously from that obtained by considering a beam model to the value given by the linear plate theory. This behaviour depends on section geometry, Poisson's ratio, and main curvature. A new characterizing parameter, whose relation with flexural stiffness allows a typical non-linear behaviour to be emphasized, is introduced in this work. In particular, for a given geometry and material, the flexural stiffness increases with the deflection and consequently with the load.

Application of Orthotropic Plate Theory to Windmill Blade Design

1981 ◽  
Vol 103 (4) ◽  
pp. 892-894 ◽  
Author(s):  
C. Rubin
Keyword(s):  
Free Boundary ◽  
Boundary Conditions ◽  
Closed Form ◽  
Orthotropic Plate ◽  
Plate Theory ◽  
Closed Form Solution ◽  
Layered Structures ◽  
Form Solution ◽  
Blade Design ◽  
Free Boundary Conditions

The windmill blade is treated as a semi-infinite orthotropic wedge with free-free boundary conditions. A closed form solution for the deflections and stresses is obtained as a function of the loading. The loading may be quite general. Results for three different materials which are commonly used for windmill blades (aluminum, sitka spruce, and fiberglass) are obtained. Applications also include ribbed, corrugated, and layered structures. In addition, other types of boundary conditions may be used to obtain solutions to a wide variety of other orthotropic plate problems.

On the buckling analysis of isotropic, transversely isotropic, and laminated rectangular plates via Reddy plate theory: an exact closed-form procedure

2011 ◽  
Vol 226 (5) ◽  
pp. 1210-1224 ◽  
Author(s):  
Sh Hosseini-Hashemi ◽  
S R Atashipour ◽  
M Fadaee
Keyword(s):  
Closed Form ◽  
Plate Theory ◽  
Closed Form Solution ◽  
Shear Deformation Theory ◽  
Transversely Isotropic ◽  
Form Solution ◽  
Laminated Plates ◽  
Rectangular Plates ◽  
Third Order ◽  
Solution Methods

Based on Reddy's third-order shear deformation theory, an exact closed-form solution is proposed to describe linear buckling of transversely isotropic laminated rectangular plates under either mono- or bi-axial compressive in-plane loads. To this end, the coupled governing equations are exactly converted to two sets of uncoupled equations for in-plane and transverse deformations of symmetric laminated plates. The new uncoupled equations are analytically solved by applying both Navier and Lévy-type solution methods. The validity and high accuracy of the current exact solution are evaluated by comparing the present results with their counterparts reported in literature.

Closed-Form, Six-Slab, Thick-Plate Solution for Analysis of Edge Slab of Concrete Pavement

2005 ◽  
Vol 1919 (1) ◽  
pp. 2-15
Author(s):  
Liu Wei ◽  
T. F. Fwa
Keyword(s):  
Closed Form ◽  
Thick Plate ◽  
Plate Theory ◽  
Closed Form Solution ◽  
Form Solution ◽  
Concrete Pavement ◽  
Winkler Foundation ◽  
Critical Stresses ◽  
Jointed Concrete Pavement ◽  
Fundamental Equations

The development and application of a theoretical closed-form solution of a six-slab, thick-plate model for the structural design and analysis of an edge slab in jointed concrete pavement subjected to vertical loads are described. The jointed concrete pavement system is idealized as a six-slab system resting on a Winkler foundation. The six slabs are arranged in two rows with three slabs in each row. The loaded slab of interest is represented by a middle slab with five surrounding slabs to consider the effects of jointed pavement system. Fundamental equations of the proposed model were derived from thick-plate theory. Solutions of the fundamental equations were obtained by superposition of the solutions of appropriate elemental slabs. The validity of the proposed solutions was checked against finite element solutions. The six-slab model was applied to analyze the critical stresses and deflections of an edge slab under the following three loading conditions: interior, edge, and corner loadings. Comparisons of the computed critical stresses and deflections were made with Westergaard's solutions. Westergaard's solutions were found to overestimate the maximum bending stresses and deflections for large slabs but to tend to underestimate these pavement responses for small slabs. The likelihood of underestimation by Westergaard's solutions also increased as the load transfer efficiency of pavement joints fell.

A Closed-Form Solution for Thermal Buckling of Cross-Ply Piezolaminated Plates

2016 ◽  
Vol 16 (03) ◽  
pp. 1450112 ◽  
Author(s):  
Mehdi Bohlooly ◽  
Babak Mirzavand
Keyword(s):  
Closed Form ◽  
Plate Theory ◽  
Ritz Method ◽  
Closed Form Solution ◽  
Laminated Composite ◽  
Composite Plates ◽  
Form Solution ◽  
Thermal Buckling ◽  
Closed Form Solutions ◽  
Piezoelectric Layers

A thermal buckling analysis is presented for simply-supported rectangular symmetric cross-ply laminated composite plates that are integrated with surface-mounted piezoelectric actuators and subjected to the combined action of thermal load and constant applied actuator voltage. The material properties of the composite and piezoelectric layers are assumed to be functions of temperature. Derivations of the equations are based on the classical laminated plate theory, using the von-Karman nonlinear kinematic relations. The Ritz method is adopted to obtain closed-form solutions for the critical buckling temperature. Numerical examples are presented to verify the proposed method. The effects of the applied actuator voltage, plate geometry and stacking sequence of laminates are investigated.

On a Closed-Form Solution of Prandtl's System of Equations

2013 ◽  
Vol 40 (2) ◽  
pp. 106-114
Author(s):  
J. Venetis ◽  
Aimilios (Preferred name Emilios) Sideridis
Keyword(s):  
Closed Form ◽  
Closed Form Solution ◽  
Form Solution ◽  
System Of Equations
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