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1

A method for comparison of large deflection in beams

Taghipour Yasser, Darfarin Sara

International Journal of Applied Mechanics and Engineering

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2022

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Vol. 27, no. 4

179--193

EN

The deflection analysis of beams has been recently an active area of research. The large deflection of beams refers to deflections occurring due to large displacements and small strains. This type of deflection has been one of the areas of interest in the development of beam deformation methods. The wide diversity of beam deformation methods highlights the importance of their comparison to further elucidate the properties and features of each method and determine their benefits and limitations. In this study, a new comparison model is introduced which involves three steps, instead of only comparing final results for verification in common studies. In the first step, a complete comparison is made based on the assumptions and approximations of each method of the kinematics of deformation, displacement, and strain fields. After selecting the most accurate method in the first step, the displacement functions are determined by polynomial approximation under different loading and support conditions based on the selected method. In the third step, the displacement functions are used to calculate the strains in each method. The conclusion is based on comparing the strains. This comparative model can be used as a benchmark to compare different theories of deformation analysis.

2

Numerical Analysis of Large Deflections of a Flat Textile Structure with Variable Bending Rigidity and Verification of Results Using Fem Simulation

Szablewski Piotr

Autex Research Journal

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2021

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Vol. 21, no. 1

108--114

EN

The paper presents the numerical modeling of large deflections of a flat textile structure subjected to a constant force acting on the free end. It was assumed that the examined structure is inextensible. The effect of the structure's own weight was also taken into account. In order to solve the problem, the flat textile structure was modeled using the heavy elastica theory. An important element of the analysis involves taking into account the variable bending rigidity of the examined textile structure along its length, which is often found in this type of products. The function of variable bending rigidity was assumed in advance. Numerical calculations were carried out in the Mathematica environment using the shooting method for the boundary value problem. The obtained results were verified using the finite element method.

3

Ritz method for large deflection of orthotropic thin plates with mixed boundary conditions

Al-Shugaa Madyan A., Al-Gahtani Husain J., Musa Abubakr E.S.

Journal of Applied Mathematics and Computational Mechanics

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2020

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Vol. 19, nr 2

5--16

EN

In this paper, the Ritz method is developed for the analysis of thin rectangular orthotropic plates undergoing large deflection. The trial functions approximating the plate lateral and in-plane displacements are represented by simple polynomials. The nonlinear algebraic equations resulting from the application of the concept of minimum potential energy of the orthotropic plate are cast in a matrix form. The developed matrix form equations are then implemented in a Mathematica code that allows for the automation of the solution for an arbitrary number of the trial polynomials. The developed code is tested through several numerical examples involving rectangular plates with different aspect ratios and boundary conditions. The results of all examples demonstrate the efficiency and accuracy of the proposed method.

4

Geometrically Nonlinear Analysis of Functionally Graded Shells Based on 2-D Cosserat Constitutive Model

Daszkiewicz K., Chróścielewski J., Witkowski W.

Engineering Transactions

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2014

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Vol. 62, iss. 2

109--130

EN

In this paper geometrically nonlinear analysis of functionally graded shells in 6-parameter shell theory is presented. It is assumed that the shell consists of two constituents: ceramic and metal. The mechanical properties are graded through the thickness and are described by power law distribution. Formulation based on 2-D Cosserat constitutive model is used to derive constitutive relation for functionally graded shells. Numerical results for typical benchmark geometries of smooth and irregular FGM shells under mechanical loading are presented. The influence of power-law exponent and micropolar material constants on the overall behaviour of functionally graded shells is investigated.

5

Analysis of helical compression spring support influence on its deformation

Michalczyk K.

Archive of Mechanical Engineering

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2009

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Vol. LVI, nr 4

349-362

EN

This paper presents a new method of calculation of the change of axial twisting angle of compressed helical spring's end-coils in the case of rotary-free suports. The propriety of derived formulas was experimentally verified. The method is easy in application and gives results much closer to experiment than the presently used method that can be found in literature.

PL

W pracy zaprezentowano nową metodę obliczania kąta skręcania czół sprężyny śrubowej naciskowej pod obciążeniem dla przypadku obrotowo podatnego podparcia jej końców. Poprawność wyprowadzonych zależności zweryfikowano doświadczalnie. Metoda ta jest prosta w zastosowaniu i daje wyniki znacznie bliższe wynikom eksperymentu niż metoda znana z literatury i dotychczas stosowana.

6

Large deflection analysis of moderately thick composite plates

Tanriöver H., Senocak E.

Computer Assisted Mechanics and Engineering Sciences

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2006

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Vol. 13, No. 4

683-690

EN

Large deflection analysis of laminated composite plates is considered. The Galerkin method along with Newton-Raphson method is applied to large deflection analysis of laminated composite plates with various edge conditions. First order shear deformation theory and von Karman type nonlinearity are utilized and the governing differential eąuations are solved by choosing suitable polynomials as trial functions to ap-proximate the plate displacement functions. The solutions are compared to that of Chebyshev polynomials and finite elements. A very close agreement has been observed with these approximating methods. In the solution process, analytical computation has been done wherever it is possible, and analytical-numerical type approach has been madę for all problems.