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.

Some problems concerning the production of a linear shear flow using curved wire-gauze screens

1976 ◽  
Vol 76 (4) ◽  
pp. 689-709 ◽  
Author(s):  
I. P. Castro
Keyword(s):  
Shear Flow ◽  
Incompressible Fluid ◽  
Experimental Work ◽  
Arbitrary Shape ◽  
Practical Problem ◽  
Analytic Solution ◽  
Linear Shear ◽  
Wire Gauze ◽  
The Common ◽  
Small Shear

The flow of an incompressible fluid through a curved wire-gauze screen of arbitrary shape is reconsidered. Some inconsistencies in previously published papers are indicated and the various approximations and linearizations (some of which are necessary for a complete analytic solution) are discussed and their inadequacies demonstrated. Attention is concentrated on the common practical problem of calculating the screen shape required to produce a linear shear flow and experimental work is presented which supports the contention that the theoretical solutions proposed by Elder (1959)–subsequently discussed by Turner (1969) and Livesey & Laws (1973)-and Lau & Baines (1968) are inadequate, although, for the case of small shear, Elder's theory appears to be satisfactory. Since, in addition, there are inevitable difficulties concerning both the value of the deflexion coefficient appropriate to any particular screen and inhomogeneities in the screen itself, it is concluded that the preparation of a curved screen to produce the commonly required moderate to large linear shear flow is bound to be somewhat empirical and should be attempted with caution.

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 Properties of the post-inspiral common envelope ejecta – I. Dynamical and thermal evolution

2019 ◽  
Vol 489 (3) ◽  
pp. 3334-3350 ◽  
Author(s):  
Roberto Iaconi ◽  
Keiichi Maeda ◽  
Orsola De Marco ◽  
Takaya Nozawa ◽  
Thomas Reichardt
Keyword(s):  
Thermal Evolution ◽  
Kinematic Model ◽  
Numerical Approach ◽  
Binary Interaction ◽  
Recombination Energy ◽  
Compact Binaries ◽  
Common Envelope ◽  
Type Ia ◽  
The Common ◽  
Ia Supernovae

ABSTRACT We investigate the common envelope binary interaction, that leads to the formation of compact binaries, such as the progenitors of Type Ia supernovae or of mergers that emit detectable gravitational waves. In this work, we diverge from the classic numerical approach that models the dynamic inspiral. We focus instead on the asymptotic behaviour of the common envelope expansion after the dynamic inspiral terminates. We use the SPH code phantom to simulate one of the set-ups from Passy et al., with a 0.88 M⊙, 83 R⊙ RGB primary and a 0.6 M⊙ companion, then we follow the ejecta expansion for 50 yr. Additionally, we utilize a tabulated equation of state including the envelope recombination energy in the simulation (Reichardt et al.), achieving a full unbinding. We show that, as time passes, the envelope’s radial velocities dominate over the tangential ones, hence allowing us to apply an homologous expansion kinematic model to the ejecta. The external layers of the envelope become homologous as soon as they are ejected, but it takes 5000 d (14 yr) for the bulk of the unbound gas to achieve the homologously expanding regime. We observe that the complex distribution generated by the dynamic inspiral evolves into a more ordered, shell-like shaped one in the asymptotic regime. We show that the thermodynamics of the expanding envelope are in very good agreement with those expected for an adiabatically expanding sphere under the homologous condition and give a prediction for the location and temperature of the photosphere assuming dust to be the main source of opacity. This technique ploughs the way to determining the long-term light behaviour of common envelope transients.

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.

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