Asymptotic Energy Behavior of Two Classical Intermediate Benchmark Shell Problems

We consider two classical problems which are widely used as benchmark tests for shell numerical methods: the Scordelis–Lo roof and the pinched roof. Due to the particular load and boundary conditions applied, neither belongs to the well-known classes of purely bending or purely membrane dominated shells. Consequently the asymptotic energy norm behavior, which is useful not only because it represents the structure stiffness, but also for numerical comparison purposes, is not a priori known. In this work, using space interpolation techniques and a recently developed "intermediate" shell theory, the asymptotic energy behavior of both problems is found analytically. The results are in agreement with the numerical estimates obtained in other papers.

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Numerical evaluation of the asymptotic energy behavior of intermediate shells with application to two classical benchmark tests

Computers & Structures ◽

10.1016/j.compstruc.2003.10.022 ◽

2004 ◽

Vol 82 (6) ◽

pp. 525-534 ◽

Cited By ~ 5

Author(s):

L. Beirão da Veiga ◽

C. Chinosi

Keyword(s):

Numerical Evaluation ◽

Benchmark Tests ◽

Energy Behavior ◽

Asymptotic Energy

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Upon Impact Numerical Modeling of Foam Materials

Materiale Plastice ◽

10.37358/mp.17.2.4816 ◽

2017 ◽

Vol 54 (2) ◽

pp. 195-202

Author(s):

Vasile Nastasescu ◽

Silvia Marzavan

Keyword(s):

Finite Element Method ◽

Finite Element ◽

Numerical Modeling ◽

Numerical Analysis ◽

Numerical Methods ◽

Boundary Conditions ◽

General Character ◽

Foam Material ◽

Various Boundary Conditions ◽

Specific Behaviour

The paper presents some theoretical and practical issues, particularly useful to users of numerical methods, especially finite element method for the behaviour modelling of the foam materials. Given the characteristics of specific behaviour of the foam materials, the requirement which has to be taken into consideration is the compression, inclusive impact with bodies more rigid then a foam material, when this is used alone or in combination with other materials in the form of composite laminated with various boundary conditions. The results and conclusions presented in this paper are the results of our investigations in the field and relates to the use of LS-Dyna program, but many observations, findings and conclusions, have a general character, valid for use of any numerical analysis by FEM programs.

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Non-Deteriorating Numerical Methods and Artificial Boundary Conditions for the Long-Term Integration of Maxwell's Equations

10.21236/ada427296 ◽

2004 ◽

Author(s):

Semyon T. Tsynkov

Keyword(s):

Numerical Methods ◽

Boundary Conditions ◽

Maxwell’S Equations ◽

Maxwell's Equations ◽

Artificial Boundary ◽

Artificial Boundary Conditions

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Vibration of rotating circular cylindrical shells with distributed springs

Journal of Mechanics ◽

10.1093/jom/ufab008 ◽

2021 ◽

Vol 37 ◽

pp. 346-358

Author(s):

Fuchun Yang ◽

Xiaofeng Jiang ◽

Fuxin Du

Keyword(s):

Boundary Conditions ◽

Galerkin Method ◽

Shell Theory ◽

Rotation Speed ◽

Cylindrical Shells ◽

Free Vibrations ◽

Governing Equations ◽

Natural Response ◽

Circular Cylindrical Shells ◽

The Galerkin Method

Abstract Free vibrations of rotating cylindrical shells with distributed springs were studied. Based on the Flügge shell theory, the governing equations of rotating cylindrical shells with distributed springs were derived under typical boundary conditions. Multicomponent modal functions were used to satisfy the distributed springs around the circumference. The natural responses were analyzed using the Galerkin method. The effects of parameters, rotation speed, stiffness, and ratios of thickness/radius and length/radius, on natural response were also examined.

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On Fourier Series in Eigenfunctions of Elliptic Boundary Value Problems

Georgian Mathematical Journal ◽

10.1515/gmj.2003.401 ◽

2003 ◽

Vol 10 (3) ◽

pp. 401-410

Author(s):

M. S. Agranovich ◽

B. A. Amosov

Keyword(s):

Fourier Series ◽

Boundary Conditions ◽

Fourier Coefficients ◽

Elliptic Boundary ◽

A Priori ◽

Adjoint Problem ◽

Elliptic Boundary Value ◽

Right Hand ◽

The Difference ◽

The Right

Abstract We consider a general elliptic formally self-adjoint problem in a bounded domain with homogeneous boundary conditions under the assumption that the boundary and coefficients are infinitely smooth. The operator in 𝐿2(Ω) corresponding to this problem has an orthonormal basis {𝑢𝑙} of eigenfunctions, which are infinitely smooth in . However, the system {𝑢𝑙} is not a basis in Sobolev spaces 𝐻𝑡 (Ω) of high order. We note and discuss the following possibility: for an arbitrarily large 𝑡, for each function 𝑢 ∈ 𝐻𝑡 (Ω) one can explicitly construct a function 𝑢0 ∈ 𝐻𝑡 (Ω) such that the Fourier series of the difference 𝑢 – 𝑢0 in the functions 𝑢𝑙 converges to this difference in 𝐻𝑡 (Ω). Moreover, the function 𝑢(𝑥) is viewed as a solution of the corresponding nonhomogeneous elliptic problem and is not assumed to be known a priori; only the right-hand sides of the elliptic equation and the boundary conditions for 𝑢 are assumed to be given. These data are also sufficient for the computation of the Fourier coefficients of 𝑢 – 𝑢0. The function 𝑢0 is obtained by applying some linear operator to these right-hand sides.

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