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1

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.

2

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.

3

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.

4

Obliczanie odkształceń sprężystej próbki przy użyciu programu dostępnego online

Drozd K.

Logistyka

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2010

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nr 6

PL

W pracy przedstawiono rozwiązanie analityczne równania różniczkowego ugięcia płaskiej belki wspornikowej obciążonej siłą pionową oraz dokonano analizy możliwości jego zastosowania do obliczeń ugięcia próbek stosowanych do badań wytrzymałości zmęczeniowej. Całkowanie równań prowadzi do wyznaczenia ścisłej matematycznie zależności kąta ugięcia od bieżącej zmiennej niezależnej (odległości od początku układu współrzędnych). Zastosowanie znanego rozwiązania, w przypadku występowania dużych ugięć belki, prowadzi do znacznych błędów, przekraczających 11% wartości kąta ugięcia.

EN

Analytical solution of differential equation of flat elastic bracket distortions' under vertical force is shown in the paper. Result of integration of the equation is coincidence only for relation between deflection angle and distance from fixed point of beam. In the case of using simple solution of equation to analyze deflection of a spring, the error may be over 11% of deflection angle value.

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.