Impulsive Deformation of Mirsky-Herrmann’s Thick Cylindrical Shells by a Numerical Method

1973 ◽  
Vol 40 (4) ◽  
pp. 1009-1016 ◽  
Author(s):  
M. Ziv ◽  
M. Perl
Keyword(s):  
Shell Theory ◽  
Pulse Velocity ◽  
Normal Strain ◽  
Finite Difference Technique ◽  
Characteristics Method ◽  
Transverse Normal Stress ◽  
Infinite Cylindrical Shell ◽  
Shell Equations ◽  
Thickness Parameter ◽  
Transverse Normal Strain

The transient response of a thick elastic semi-infinite cylindrical shell subjected to impulsive step loads is obtained. This work presents solutions to two boundary-value problems. First, the shell is exposed to an axially step pulse velocity load while second, the pulse is applied radially to the shell. The influence of the transverse normal stress and the transverse normal strain on the deformation is being studied in great detail. The shell theory employed is based on the thick-shell equations derived by Mirsky and Herrmann, which comprise these transversal effects. These equations are solved by the characteristics method, while integration is carried out by the finite-difference technique. The results also present the influence of the thickness parameter (h/R) on the solution. Comparisons are made to solutions of other shell theories which neglect the transversal effects. Major conclusions show the existence of an important influence of the transverse normal strain on the deformation.

A Refined Theory for Laminated Anisotropic, Cylindrical Shells

1974 ◽  
Vol 41 (2) ◽  
pp. 471-476 ◽  
Author(s):  
J. M. Whitney ◽  
C.-T. Sun
Keyword(s):  
Shear Deformation ◽  
Shell Theory ◽  
Theory Of Elasticity ◽  
Small Radius ◽  
Refined Theory ◽  
Normal Strain ◽  
Governing Equations ◽  
Transverse Normal Strain ◽  
Anisotropic Cylindrical Shell ◽  
Good Agreement

A set of governing equations and boundary conditions are derived which describe the static deformation of a laminated anisotropic cylindrical shell. The theory includes both transverse shear deformation and transverse normal strain, as well as expansional strains. The validity of the theory is assessed by comparing solutions obtained from the shell theory to results obtained from exact theory of elasticity. Reasonably good agreement is observed and both shear deformation and transverse normal strain are shown to be of importance for shells having a relatively small radius-to-thickness ratio.

On Free Vibrations of an Embedded Anisotropic Spherical Shell

1997 ◽  
Vol 119 (4) ◽  
pp. 481-487 ◽  
Author(s):  
W. Q. Chen ◽  
H. J. Ding
Keyword(s):  
Spherical Shell ◽  
Elastic Medium ◽  
Shell Theory ◽  
Three Dimensional ◽  
Homogeneous Solution ◽  
Free Vibrations ◽  
Normal Strain ◽  
Auxiliary Variables ◽  
Transverse Normal Strain ◽  
Isotropic Spherical Shell

In this paper, free vibrations of a spherically isotropic spherical shell embedded in an elastic medium of Pasternak type are studied by using a six-mode shell theory that includes effects of shear deformation, rotary inertia, and transverse normal strain. The separable homogeneous solution for displacements and stresses in a deep spherical shell is derived and two classes of vibrations are obtained by the introduction of five auxiliary variables. Numerical results are compared with those predicted by two simpler shell theories mentioned in the paper and those by three-dimensional elastic theory.

Three-Dimensional and Shell-Theory Analysis of Elastic Waves in a Hollow Sphere: Part 1—Analytical Foundation

1969 ◽  
Vol 36 (3) ◽  
pp. 431-439 ◽  
Author(s):  
A. H. Shah ◽  
C. V. Ramkrishnan ◽  
S. K. Datta
Keyword(s):  
Elastic Waves ◽  
Shell Theory ◽  
Three Dimensional ◽  
Frequency Equation ◽  
Wave Number ◽  
Normal Strain ◽  
Theory Analysis ◽  
Analytical Foundation ◽  
Transverse Normal Strain ◽  
Approximate Equations

In Part 1 of this paper an exact analysis of the nonaxisymmetric wave propagation in a hollow elastic sphere is presented. It is found that the characteristic frequency equation is independent of the longitudinal wave number. Approximate equations for thin shells and membranes are derived by way of asymptotic expansions. In general, the vibrations fall into two distinct classes, one of which is equivoluminal. Also included in the paper is a six-mode shell theory in which the effects of transverse normal strain are included. A technique due to van der Neut is used to separate the governing partial differential equations whereby two frequency equations corresponding to the two classes of vibrations are obtained.

A refined sinusoidal model for functionally graded plates subjected to thermomechanical loading

2018 ◽  
Vol 53 (14) ◽  
pp. 1883-1896
Author(s):  
Ren Xiaohui ◽  
Wu Zhen
Keyword(s):  
Functionally Graded Material ◽  
Thermal Loading ◽  
Functionally Graded ◽  
Normal Strain ◽  
Sinusoidal Model ◽  
Proposed Model ◽  
Graded Material ◽  
Plane Displacement ◽  
Stress Free Boundary ◽  
Transverse Normal Strain

A refined sinusoidal model considering transverse normal strain has been developed for thermoelastic analysis of functionally graded material plate. Although transverse normal strain has been considered, the additional displacement parameters are not increased as transverse normal strain only includes the thermal expansion coefficient and thermal loading. Moreover, the merit of the previous sinusoidal model satisfying tangential stress-free boundary conditions on the surfaces can be maintained. It is important that the effects of transverse normal thermal deformation are incorporated in the in-plane displacement field, which can actively influence the accuracy of in-plane stresses. To assess the performance of the proposed model, the thermoelastic behaviors of functionally graded material plates with various configurations have been analyzed. Without increase of displacement variables, accuracy of the proposed model can be significantly improved by comparing to the previous sinusoidal model. Agreement between the present results and quasi-dimensional solutions are very good, and the proposed model only includes the five displacement variables which can illustrate the accuracy and effectiveness of the present model. In addition, new results using several models considered in this paper have been presented, which can serve as a reference for future investigations.

Boundary Integral Equation Methods for a Refined Model of Elastic Plates

2006 ◽  
Vol 11 (6) ◽  
pp. 642-654
Author(s):  
Radu Mitric ◽  
Christian Constanda
Keyword(s):  
Integral Equation ◽  
Boundary Integral Equation ◽  
Boundary Integral ◽  
Normal Strain ◽  
Elastic Plates ◽  
Equilibrium Equations ◽  
Neumann Problems ◽  
Integral Equation Methods ◽  
Transverse Normal Strain ◽  
System Of Equilibrium Equations

A theory of bending of elastic plates is considered, in which the effect of transverse shear deformation and transverse normal strain are taken into account through a specific form of the displacement field. It is shown that the system of equilibrium equations is elliptic and that Betti and Somigliana formulae can be established, which permit the solution of the interior and exterior Dirichlet and Neumann problems by means of boundary integral equation methods.

A Review of Tubular Conical Transition Strength Design Equations

2020 ◽  
Author(s):  
Albert Ku ◽  
Jieyan Chen ◽  
Bernard Cyprian
Keyword(s):  
Thin Shell ◽  
Shell Theory ◽  
Yield Criterion ◽  
Plasticity Theory ◽  
Transition Strength ◽  
Ultimate Capacity ◽  
Design Standards ◽  
Fem Simulations ◽  
Column Type ◽  
Shell Equations

Abstract This paper consists of two parts. Part one presents a thin-shell analytical solution for calculating the conical transition junction loads. Design equations as contained in the current offshore standards are based on Boardman’s 1940s papers with beam-column type of solutions. Recently, Lotsberg presented a solution based on shell theory, in which both the tubular and the cone were treated with cylindrical shell equations. The new solution as presented in this paper is based on both cylindrical and conical shell theories. Accuracies of these various derivations will be compared and checked against FEM simulations. Part 2 of this paper is concerned with the ultimate capacity equations of conical transitions. This is motivated by the authors’ desire to unify the apparent differences among the API 2A, ISO 19902 and NORSOK design standards. It will be shown that the NORSOK provisions are equivalent to the Tresca yield criterion as derived from shell plasticity theory. API 2A provisions are demonstrated to piecewise-linearly approximate this Tresca yield surface with reasonable consistency. The 2007 edition of ISO 19902 will be shown to be too conservative when compared to these other two design standards.

BENDING OF FGM PLATES BY A SIMPLIFIED FOUR-UNKNOWN SHEAR AND NORMAL DEFORMATIONS THEORY

2013 ◽  
Vol 05 (02) ◽  
pp. 1350020 ◽  
Author(s):  
ASHRAF M. ZENKOUR
Keyword(s):  
Virtual Work ◽  
Plate Thickness ◽  
Present Theory ◽  
Normal Strain ◽  
Principle Of Virtual Work ◽  
Governing Equations ◽  
Shear Strains ◽  
Transverse Normal Strain ◽  
Transverse Shear Strains ◽  
Bending Response

The bending response of FGM plates is presented based upon a simplified shear and normal deformations theory. The present simplified theory is accounted for an adequate distribution of transverse shear strains through the plate thickness and tangential stress-free on the plate surfaces. The effect of transverse normal strain is also included. The number of unknown functions involved here is only four as against six in case of other shear and normal deformations theories. The principle of virtual work is employed to derive the governing equations. A comparison with the corresponding results is made to check the accuracy and efficiency of the present theory. Additional results for all stresses are investigated through-the-thickness of the FGM plate.

On the Significance of the Inclusion of the Effect of Transverse Normal Strain in Problems Involving Beams With Surface Constraints

1975 ◽  
Vol 42 (1) ◽  
pp. 127-132 ◽  
Author(s):  
F. Essenburg
Keyword(s):  
Shear Deformation ◽  
General Problem ◽  
Transverse Shear ◽  
Beam Theory ◽  
Transverse Shear Deformation ◽  
Normal Strain ◽  
Rectangular Section ◽  
Surface Constraints ◽  
Transverse Normal Strain

The general problem of a beam of rectangular section with displacement components prescribed over portions of its top and bottom surfaces is considered. A beam theory which includes the effect of transverse normal strain (as well as the effect of transverse shear deformation) is developed and the advantages of applying this theory to the class of problems considered is examined by means of an example.

scholarly journals Effects of transverse normal strain on bending of laminated composite beams

2018 ◽  
Vol 40 (3) ◽  
pp. 217-232 ◽  
Author(s):  
Trung-Kien Nguyen ◽  
Ngoc-Duong Nguyen
Keyword(s):  
Ritz Method ◽  
Laminated Composite ◽  
Beam Theory ◽  
Composite Beams ◽  
Normal Strain ◽  
Shape Functions ◽  
Height Ratio ◽  
Order Variation ◽  
Transverse Normal Strain ◽  
Laminated Composite Beams

Effect of transverse normal strain on bending of laminated composite beams is proposed in this paper. A Quasi-3D beam theory which accounts for a higher-order variation of both axial and transverse displacements is used to consider the effects of both transverse shear and normal strains on bending behaviours of laminated composite beams. Ritz method is used to solve characteristic equations in which trigonometric shape functions are proposed. Numerical results for different boundary conditions are presented to compare with those from earlier works, and to investigate the effects of thickness stretching, fibre angles, span-to-height ratio and material anisotropy on the displacement and stresses of laminated composite beams.

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