Plane Stress Analysis of End-Loaded Orthotropic Curved Beams of Constant Thickness With Applications to Full Rings

1998 ◽  
Vol 120 (2) ◽  
pp. 368-374 ◽  
Author(s):  
N. Tutuncu
Keyword(s):  
Plane Stress ◽  
Plane Elasticity ◽  
Isotropic Case ◽  
Constant Thickness ◽  
Curved Beams ◽  
Degree Of Anisotropy ◽  
Stress Functions ◽  
Elasticity Solutions ◽  
Two Parameters ◽  
Plane Stress Analysis

Plane elasticity solutions using stress functions for stresses and displacements in orthotropic curved beams subjected to end moment and force loadings are presented. Applications to curved beams with straight portions and full rings are considered. The results are compared with the isotropic case. Two parameters, which essentially measure the degree of anisotropy, each pertaining to a different loading state are defined and their effects on the stress and displacement distributions are discussed. It has been shown that increasing these parameters reduced the stresses in the members.

Exact Elasticity Solutions for Stresses and Deflections in Curved Beams and Rings of Exponential and T-Sections

1991 ◽  
Author(s):  
Cemil Bagci
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Plane Stress ◽  
Numerical Results ◽  
Neutral Axis ◽  
Curved Beams ◽  
Equilibrium Stress ◽  
Different Boundary Conditions ◽  
Stress Functions ◽  
Elasticity Solutions

Abstract Exact elasticity solutions for stresses and deflections (displacements) in curved beams and rings of varying thicknesses are developed using polar elasticity and state of plane stress. Basic forms of differential equations of equilibrium, stress functions, and differential equations of compatibility are given. They are solved to develop expressions for radial, tangential, and shearing stresses for moment, force, and combined loadings. Neutral axis location for each type of loading is determined. Expressions for displacements are developed utilizing strain-displacement relationships of polar elasticity satisfying boundary conditions on displacements. In case of full rings stresses are as in curved beams with properly defined moment loading, but displacements differ satisfying different boundary conditions. The developments for constant thicknesses are used to develop solutions for curved beams and rings with T-sections. Comparative numerical results are given.

Exact Elasticity Solutions for Stresses and Deflections in Curved Beams and Rings of Exponential and T-Sections

1993 ◽  
Vol 115 (3) ◽  
pp. 346-358 ◽  
Author(s):  
C. Bagci
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Plane Stress ◽  
Numerical Results ◽  
Neutral Axis ◽  
Curved Beams ◽  
Equilibrium Stress ◽  
Different Boundary Conditions ◽  
Stress Functions ◽  
Elasticity Solutions

Exact elasticity solutions for stresses and deflections (displacements) in curved beams and rings of varying thicknesses are developed using polar elasticity and state of plane stress. Basic forms of differential equations of equilibrium, stress functions, and differential equations of compatibility are given. They are solved to develop expressions for radial, tangential, and shearing stresses for moment, force, and combined loadings. Neutral axis location for each type of loading is determined. Expressions for displacements are developed utilizing strain-displacement relationships of polar elasticity satisfying boundary conditions on displacements. In case of full rings stresses are as in curved beams with properly defined moment loading, but displacements differ satisfying different boundary conditions. The developments for constant thicknesses are used to develop solutions for curved beams and rings with T-sections. Comparative numerical results are given.

Buckling Characteristics of Laminated Functionally-Graded CNT-Reinforced Composite Plate under Nonuniform Uniaxial and Biaxial In-Plane Edge Loads

2019 ◽  
Vol 20 (02) ◽  
pp. 2050022 ◽  
Author(s):  
Balakrishna Adhikari ◽  
B. N. Singh
Keyword(s):  
Differential Equations ◽  
Plane Stress ◽  
Lagrange Equation ◽  
Shear Deformation Theory ◽  
Plane Elasticity ◽  
Functionally Graded ◽  
Reinforced Composite ◽  
General Eigenvalue Problem ◽  
The Impact ◽  
Plane Stress Analysis

In this paper, the buckling response of laminated functionally-graded CNT-reinforced composite (FG-CNTRC) plate structure is predicted under various types of non-uniform edge compression loading. For the finite element (FE) discretization of the plate, a nine degree of freedom (DOFs)-type polynomial-based higher-order shear deformation theory (HSDT) is considered. The application of non-uniform edge load causes the in-plane stress distribution to be non-uniform. Hence, the in-plane stresses need to be evaluated prior to the buckling analysis. These in-plane stresses are calculated using the in-plane stress analysis method by FE approach or the in-plane elasticity approach. The differential equations are obtained by employing the Lagrange equation of motion and solved as a general eigenvalue problem, after the differential equations are converted into homogeneous equations by means of FE procedure. The accuracy and adaptability of the present model are validated by comparing the present result with the available literature. Further, the impact on the buckling response of the laminated FG-CNTRC plate is investigated by various parameters such as span thickness ratio, aspect ratio, various edge constraints, and different types of non-uniform edge load, CNT fiber gradation and temperature dependency material properties.

General Solutions of the Equations of Elasticity and Consolidation for a Porous Material

1956 ◽  
Vol 23 (1) ◽  
pp. 91-96
Author(s):  
M. A. Biot
Keyword(s):  
Stress Field ◽  
Porous Material ◽  
Elastic Material ◽  
Displacement Field ◽  
Theory Of Elasticity ◽  
Isotropic Case ◽  
General Solutions ◽  
General Properties ◽  
Stress Functions

Abstract Equations of elasticity and consolidation for a porous elastic material containing a fluid have been previously established (1, 5). General solutions of these equations for the isotropic case are developed, giving directly the displacement field or the stress field in analogy with the Boussinesq-Papkovitch solution and the stress functions of the theory of elasticity. General properties of the solutions also are examined and the viewpoint of eigenfunctions in consolidation problems is introduced.

Accurate Calculation of Stress Distributions in Multiholed Plates

1965 ◽  
Vol 87 (3) ◽  
pp. 331-335 ◽  
Author(s):  
L. E. Hulbert ◽  
F. W. Niedenfuhr
Keyword(s):  
Computer Program ◽  
Plane Stress ◽  
Symmetric Groups ◽  
Thin Plates ◽  
Stress Distributions ◽  
Accurate Calculation ◽  
Point Matching ◽  
Shallow Shells ◽  
Matching Technique ◽  
Stress Functions

This paper discusses the application of the point-matching technique in obtaining the solution of many problems involving multiholed thin plates undergoing generalized plane stress. The stress functions appropriate to plates with symmetric groups of holes are described. A large number of problems solved by a computer program are described and compared with published results. Problems are solved also for which there are no known published results. Two interesting new problems are discussed in detail. The results show the power and flexibility of the technique. The extension of the methods to permit the solution of problems in the deflection of thin, multiholed plates and shallow shells is discussed.

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