scholarly journals Development of thin shell equations for reactor subassembly dynamics. [LMFBR]

1976 ◽  
Author(s):  
G. Devault ◽  
P. Blewett
Keyword(s):  
Thin Shell ◽  
Shell Equations

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.

scholarly journals Approximation of Linear Elastic Shells by Curved Triangular Finite Elements Based on Elastic Thick Shells Theory

2016 ◽  
Vol 2016 ◽  
pp. 1-12 ◽  
Author(s):  
Joseph Nkongho Anyi ◽  
Robert Nzengwa ◽  
Jean Chills Amba ◽  
Claude Valery Abbe Ngayihi
Keyword(s):  
Thin Shell ◽  
Thick Shell ◽  
Absolute Value ◽  
Linear Elastic ◽  
Limit Value ◽  
Shell Equations ◽  
Third Fundamental Form ◽  
Nodal Displacements ◽  
Thick Shells ◽  
Thin Shell Theory

We have developed a curved finite element for a cylindrical thick shell based on the thick shell equations established in 1999 by Nzengwa and Tagne (N-T). The displacement field of the shell is interpolated from nodal displacements only and strains assumption. Numerical results on a cylindrical thin shell are compared with those of other well-known benchmarks with satisfaction. Convergence is rapidly obtained with very few elements. A scaling was processed on the cylindrical thin shell by increasing the ratioχ=h/2R(half the thickness over the smallest radius in absolute value) and comparing results with those obtained with the classical Kirchhoff-Love thin shell theory; it appears that results diverge at2χ=1/10=0.316because of the significant energy contribution of the change of the third fundamental form found in N-T model. This limit value of the thickness ratio which characterizes the limit between thin and thick cylindrical shells differs from the ratio 0.4 proposed by Leissa and 0.5 proposed by Narita and Leissa.

An Exact Modal Analysis of the Static Deformation of Long Cylinders and Rings

1984 ◽  
Vol 106 (4) ◽  
pp. 348-353 ◽  
Author(s):  
H. D. Fisher
Keyword(s):  
Continuous Function ◽  
General Solution ◽  
Cross Section ◽  
Thin Shell ◽  
Present Theory ◽  
Angular Variable ◽  
Arbitrary Angle ◽  
Shell Equations ◽  
Modal Solution ◽  
Long Cylinder

This paper presents a static, modal solution of Flugge’s thin shell equations for the cases of a ring or a long cylinder in a state of plane strain. The solution derived here enables the design analyst to compute the deflection resulting from concentrated loads applied in the plane of the cross section at an arbitrary angle to the circumference of the shell and to eliminate the error which results, in certain cases, from employing a previously derived inextensional analysis. A general solution is given for the case of any number of concentrated radial, tangential, and moment loads. The method of analysis for loadings that are a continuous function of the angular variable is also illustrated via a specific example. Numerical results compare solutions obtained with the present theory with those computed by invoking the assumption of inextensional deformation.

Patching Model for Acoustoelastic Scattering

1995 ◽  
Author(s):  
David A. Sachs
Keyword(s):  
Electromagnetic Scattering ◽  
Acoustic Waves ◽  
Thin Shell ◽  
Practical Problem ◽  
Numerical Approach ◽  
Incident Plane ◽  
Finite Element Calculations ◽  
The Common ◽  
Shell Equations ◽  
Finite Cylindrical Shell

Abstract Faceting models have long been used in electromagnetic scattering to achieve target shape generality. An analogous approach to acoustoelastic scattering from submerged shells has been developed. Generalized asymptotic (ray) solutions of the thin shell equations for smooth shells, developed by Norris and Rebinsky, are applied to a discretized geometry representation to analyze the membrane wave contributions to the scattered field from shells excited by incident plane acoustic waves. Example results for a finite cylindrical shell with spherical endcaps are compared to Finite Element calculations. Limitations of the Norris and Rebinsky theory and of the patching methodology are discussed. A major prerequisite for further progress is a hybrid ray/numerical approach to treat the common practical problem of adjoining and interacting ray and non-ray zones.

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