Series solutions for a transversely loaded and completely clamped thick rectangular plate based on the three-dimensional theory of elasticity

1998 ◽  
Vol 68 (2) ◽  
pp. 103-121 ◽  
Author(s):  
I. A. Okumura ◽  
Y. Oguma
Keyword(s):  
Rectangular Plate ◽  
Three Dimensional ◽  
Theory Of Elasticity ◽  
Series Solutions ◽  
Dimensional Theory ◽  
Thick Rectangular Plate

Three-Dimensional Elasticity Solution of a Composite Beam

1967 ◽  
Vol 1 (2) ◽  
pp. 122-135 ◽  
Author(s):  
Staley F. Adams ◽  
M. Maiti ◽  
Richard E. Mark
Keyword(s):  
Three Dimensional ◽  
Solid Wood ◽  
Theory Of Elasticity ◽  
Orthotropic Materials ◽  
Stress And Strain ◽  
Cantilever Beams ◽  
Dimensional Theory ◽  
Reinforced Plastics ◽  
Three Dimensional Elasticity ◽  
Moduli Of Elasticity

This investigation was undertaken to develop a rigorous mathe matical solution of stress and strain for a composite pole con sisting of a reinforced plastics jacket laminated on a solid wood core. The wood and plastics are treated as orthotropic materials. The problem of bending of such poles as cantilever beams has been determined by the application of the principles of three- dimensional theory of elasticity. Values of all components of the stress tensor in cylindrical coordinates are given for the core and jacket. Exact values for the stresses have been obtained from computer results, using the basic elastic constants—Poisson's ratios, moduli of elasticity and moduli of rigidity—for each ma terial. A comparison of the numerical results of the exact solu tion with strength of materials solutions has been completed.

A Refined Theory of Elastic, Orthotropic Plates

1958 ◽  
Vol 25 (4) ◽  
pp. 437-443 ◽  
Author(s):  
S. J. Medwadowski
Keyword(s):  
Body Force ◽  
Three Dimensional ◽  
Theory Of Elasticity ◽  
Refined Theory ◽  
System Of Equations ◽  
Order Partial Differential Equation ◽  
Type Solution ◽  
Orthotropic Plates ◽  
Dimensional Theory ◽  
Nonlinear System Of Equations

Abstract A refined theory of elastic, orthotropic plates is presented. The theory includes the effect of transverse shear deformation and normal stress and may be considered a generalization of the classical theory of von Karman modified by the refinements of the Levy-Reissner-Mindlin theories. A nonlinear system of equations is derived directly from the corresponding equations of the three-dimensional theory of elasticity in which body-force terms have been retained. Next, the system of equations is linearized and reduced to a single sixth-order partial differential equation in a stress function. A Levy-type solution of this equation is discussed.

FREE VIBRATION OF AN ORTHOTROPIC HOLLOW BODY OF REVOLUTION

2005 ◽  
Vol 05 (02) ◽  
pp. 299-312
Author(s):  
D. REDEKOP
Keyword(s):  
Natural Frequencies ◽  
Differential Quadrature Method ◽  
Three Dimensional ◽  
Theory Of Elasticity ◽  
Constant Thickness ◽  
Body Of Revolution ◽  
Orthotropic Cylinder ◽  
Dimensional Theory ◽  
Hollow Cylinders ◽  
Definition Of

A method is developed to determine the natural frequencies of vibration of an orthotropic hollow body of revolution of constant thickness but of arbitrary smooth meridian. Equations are derived using the linear three-dimensional theory of elasticity, and a numerical solution is obtained using the differential quadrature method. The geometric generality of the solution is attained by delaying definition of local geometric parameters until the solution stage. Validation is by comparison with previously published results, including results for a hollow orthotropic cylinder. Sample results are given for orthotropic hollow cylinders and spherical segments, and conclusions are drawn.

Dynamic Buckling and Post-buckling of Imperfect Orthotropic Cylindrical Shells Under Mechanical and Thermal Loads, Based on the Three-Dimensional Theory of Elasticity

1999 ◽  
Vol 66 (2) ◽  
pp. 476-484 ◽  
Author(s):  
M. Shariyat ◽  
M. R. Eslami
Keyword(s):  
Circular Cylindrical Shell ◽  
Cylindrical Shells ◽  
Strain Tensor ◽  
Three Dimensional ◽  
Theory Of Elasticity ◽  
Dynamic Buckling ◽  
Curvilinear Coordinates ◽  
Thermal Loads ◽  
Dimensional Theory ◽  
Highly Nonlinear

The three-dimensional theory of elasticity in curvilinear coordinates is employed to investigate the dynamic buckling of an imperfect orthotropic circular cylindrical shell under mechanical and thermal loads. Accurate form of the strain expressions of imperfect cylindrical shells is established through employing the general Green's strain tensor for large deformations and the equations of motion are derived in terms of the second Piola-Kirchhoff stress tensor. Then, the governing equations are properly formulated and solved by means of an efficient and relatively accurate solution procedure proposed to solve the highly nonlinear equations resulting from the above analysis. The proposed formulation is very general as it can include the influence of the initial imperfections, temperature distribution, and temperature dependency of the mechanical properties of materials, effect of various end conditions, possibility of large-deformation occurrence and application of any combination of mechanical and thermal loadings. No simplifications are done when solving the resulting equations. Furthermore, in contrast to the displacement-based layer-wise theories and the three-dimensional approaches proposed so far, the stress, force and moment boundary conditions as well as the displacement type ones, can be incorporated accurately in these formulations. Finally, a few examples of mechanical and thermal buckling of some orthotropic cylindrical shells are considered and results of the present three-dimensional elasticity approach are compared with the buckling loads predicated by the Donnell's equations, some single-layer theories, some available results of the layer-wise theory and the recently published three-dimensional approaches and the accuracy of the later methods are discussed based on the exact method presented in this paper.

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