2 edition of **Asymptotic approximation in the three-dimensional theory of thin and thick elastic shells.** found in the catalog.

Asymptotic approximation in the three-dimensional theory of thin and thick elastic shells.

Hendrikus Stephanus Rutten

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Published
**1971**
by Nederlandse Boekdruk Industrie N.V. in "s-Hertogenbosch
.

Written in English

- Elastic plates and shells.,
- Approximation theory.,
- Asymptotic expansions.

**Edition Notes**

Statement | Shells of homogeneous, isotropic, elastic materials. Systematic systems of linear equations and conditions. |

Classifications | |
---|---|

LC Classifications | QA935 .R88 |

The Physical Object | |

Pagination | xv, 625 p. |

Number of Pages | 625 |

ID Numbers | |

Open Library | OL5332696M |

LC Control Number | 72185885 |

The N-T’s two-dimensional model for linear elastic thick shells has been deduced from the three-dimensional problem without any ad hoc assumption whether of geometrical or mechanical nature. The two-dimensional equations are deduced by applying asymptotic analysis on a family of variational equations obtained from an abstract scaled shell. The present study uses the procedure of asymptotic splitting (Eliseev, , ), which has already been systematically applied to the theories of thin rods with a non-homogeneous cross-section (Yeliseyev and Orlov, ), of thin-walled rods of open profile (Eliseev, ; Vetyukov, ), and of homogeneous thin plates (Eliseev, ).In .

Asymptotic approximation in the three-dimensional theory of thin and thick elastic shells: The practical classification of shell problems, shells of homogeneous, isotropic, elastic materials, systematic systems of linear equations and conditions. By H.S. (author) Rutten. Abstract. We consider a mixed boundary-value problem for the Poisson equation in a plane two-level junction Ωε, which is the union of a domain Ω0 and a large number 2N of thin .

By an asymptotic method the solution of boundary value problems of elasticity theory for isotropic, anisotropic, layered beams, plates and shells is built. The first, second and the mixed boundary problems for one-layered and multy-layered beams, plates and shells are solved. Approximation of Linear Elastic Shells by Curved Triangular Finite Elements Based on Elastic Thick Shells Theory JosephNkonghoAnyi, 1,2,3 RobertNzengwa, 1,3 JeanChillsAmba, 3 andClaudeValeryAbbeNgayihi 1,3 Department of Mechanical Engineering, National Advanced School Polytechnics, University of Yaound ´eI, P.O. Box, Yaound ´e, Cameroon.

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ASYMPTOTIC APPROXIMATION IN THE THREE-DIMENSIONAL THEORY OF THIN AND THICK ELASTIC SHELLS: The practical classification of shell problems; Shells of homogeneous, isotropic, elastic materials; Systematic systems of linear equations and conditions.

Rutten, Hendrikus Stephanus. Publisher Summary. This chapter discusses the membrane theory of shells of arbitrary shape. The membrane theory is the approximate method of analysis of thin shells based upon the assumption that the transverse shear forces N 1, N 2 vanish in the first three equilibrium equations of system.

The complete set of equations to be considered as the basic system for the analysis of shells. Asymptotic approximation in the three-dimensional theory of thin and thick elastic shells.

's-Hertogenbosch, Nederlandse Boekdruk Industrie N.V., (OCoLC) J.D. Kaplunov, E.V. Nolde, in Dynamics of Thin Walled Elastic Bodies, The main part of the book deals with the derivation of asymptotic approximations of the 3D dynamic equations of elasticity as the thickness tends to zero.

There exist four types of approximations, namely, long-wave low-frequency approximations, short-wave low. In this paper, a two-dimensional model for linear elastic thick shells is deduced from the three-dimensional problem of a shell thickness 2ε, ε > 0.

Rutten: Asymptotic approximation in the three-dimensional theory of thin and thick elastic shells. Proc. 2nd IUTAM Symposium on Shell Theory (Kopenhagen, ), pp.

Asymptotic methods play an important role in solving three-dimensional elasticity problems. The method of asymptotic integration of three-dimensional equations of elasticity theory takes an.

Rutten, H. S.: Asymptotic approximation in the three-dimensional theory of thin and thick elastic shells. Thesis Delftpublished by Netherlandse Boekdruk Industrie N.V., ’s Hertogenbosch. Google Scholar. this article is to improve on the accuracy of thin shell theory away from the shell edges.

This gives an estimate of the errors involved in the thin shell approximation and provides a theory of thicker shells. A more important purpose of our work, however, is to remedy a serious deﬁciency of the conventional shell theory for thin or thick shells.

We present a methodology for the efficient numerical solution of eigenvalue problems of full three-dimensional elasticity for thin elastic structures, such as shells, plates and rods of arbitrary geometry, discretized by the finite element method.

Such problems are solved by iterative methods, which, however, are known to suffer from slow convergence or even. CiteSeerX - Document Details (Isaac Councill, Lee Giles, Pradeep Teregowda): Abstract. We consider an elastic hollow sphere with midsurface radius R and thickness 2h which is subjected to two equal and opposite concentrated loads acting at the ends of a diameter.

The three-dimensional linear elasticity solution to this problem consists of (i) a narrow Saint Venant. An asymptotic technique is developed to analyse initial-value problems in application to the three-dimensional theory of thin elastic plates. Various sets of long-wave initial data are considered, with arbitrary distribution along the plate thickness.

Asymptotic approximation in the three-dimensional theory of thin and thick elastic shells: The practical classification of shell problems, shells of homogeneous, isotropic, elastic materials, systematic systems of linear equations and conditions: Author: Rutten, H.S. Thesis advisor: Timman, R., Bouma, A.L.

Date issued: Access: Open. According to the exact three-dimensional theory of elasticity, a shell element is considered as a volume element. We now complete the second approximation theory of the asymptotic expansion and integration procedure, which can be shown as follows: Goldenveiser, A.L., “Theory of elastic thin shells”, Pergamon Press.

[9] Ting, T.C.T. Asymptotic theory does not provide a method of evaluating the finite-sample distributions of sample statistics, however.

Non-asymptotic bounds are provided by methods of approximation theory. Examples of applications are the following.

In applied mathematics, asymptotic analysis is used to build numerical methods to approximate equation solutions. “classical” theory of plates is applicable to very thin and moderately thin plates, while “higher order theories” for thick plates are useful.

For the very thick plates, however, it becomes more difﬁcult and less useful to view the structural element as a plate - a description based on the three-dimensional theory of elasticity is. We will start with generalized Hook’s law of a three dimensional anisotropic body which is subjected to 6 different stresses and strains together with 21 elastic coefficients.

Applying equilibrium and stress displacement equations and non-dimensionalize all the variables before asymptotically expanding, we are allowed to perform the asymptotic integration.

The leading term of this approximation corresponds3 to thin shell theory. We make numerical comparisons between the predictions of our two-term re ned theory, those of thin shell theory, and those of the Reissner{Wan theory for the cases in which h=R=1=20 or 1/10, and =1=3.

When h=R=1=20, all three solutions agree closely. The ﬁrst part of this article is devoted to the three-dimensional theory of elastic bodies, from which the threedimensional theory of shells is obtained simply by replacing the reference conﬁguration of a general body with that of a shell.

The particular shape of the reference conﬁguration of the shell does not play any roˆle in this theory. Asymptotically correct, linear theory is presented for thin-walled prismatic beams made of generally anisotropic materials. Consistent use of small parameters that are intrinsic to the problem permits a natural description of all thin-walled beams within a common framework, regardless of whether cross-sectional geometry is open, closed, or strip-like.

A significant part of the book deals with problems important for engineering practice, such as: statical analysis of highly nonhomogeneous plates and shells for which common discretization techniques fail to be efficient, assessing stiffness reduction of cracked [0 0 n /90 0 m] s laminates, and assessing ultimate loads for perfectly plastic.Since our refined theory is still applicable to such moderately thick shells, the results we obtain enable us to analyze the limitations of the thin shell theory.

Furthermore, we find that the predictions of the Reissner--Wan theory are considerably closer to the true values than those of classical thin shell theory.On the basis of 3D elasticity, asymptotic solutions for buckling analysis of multilayered anisotropic conical shells under axial compression are presented.

By means of proper nondimensionalization, asymptotic expansion, and successive integration, the classical shell theory is derived as a first-order approximation to the 3D theory.