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1

Stability of Timoshenko beams with frequency andinitial stress dependent nonlocal parameters

Glabisz W., Jarczewska K., Holubowski R.

Archives of Civil and Mechanical Engineering

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2019

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Vol. 19, no. 4

1116--1126

EN

This paper presents an analysis of the stability of Timoshenko beams which uses Eringen'snonlocal elasticity theory. A numerical algorithm based on the exact solution for the freevibration of segmental Timoshenko beams was formulated. The algorithm enables one tocalculate, with any degree of accuracy, the critical load levels in the beams on the macro andnanoscale. The beams were subjected to conservative and nonconservative static loads. Thelevels of critical loads in the beams were analysed assuming a functional dependence of thenonlocal parameters on the vibrational frequency and the state of stress.

2

Imperfection sensitivity of the size-dependent postbuckling response of pressurized FGM nanoshells in thermal environments

Sahmani S., Aghdam M. M.

Archives of Civil and Mechanical Engineering

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2017

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Vol. 17, no. 3

623--638

EN

The purpose of the current study is to address the nonlinear buckling and postbuckling response of nanoscaled cylindrical shells made of functionally graded material (FGM) under hydrostatic pressure aiming to investigate the sensitivity to the initial geometric imperfection in the presence of surface effects and thermal environments. According to a power law distribution, the material properties of the FGM nanoshell are considered change through the shell thickness. Also, the change in the position of physical neutral plane corresponding to different volume fractions is taken into account to eliminate the stretching-bending coupling terms. In order to acquire the size effect qualitatively, the well-known Gurtin-Murdoch elasticity theory is incorporated within the framework of the classical shell theory. Using the variational approach, the non-classical governing equations are displayed and deduced to boundary layer type ones. Afterwards, explicit expressions for the size-dependent radial postbuckling equilibrium paths of imperfect FGM nanoshells are proposed with the aid of a perturbation-based solution methodology. It is displayed that by moving from the ceramic phase to the metal one, the critical buckling pressure decreases, but the postbuckling stiffness increases, because in contrast to the ceramic phase, the surface modulus and residual surface stress associated with the metal phase have the same sign.

3

Podstawowe właściwości mieszanek gumowych i wulkanizatów

Magryta J.

Elastomery

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2006

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T. 10, nr 1

25-32

PL

W artykule przedstawiono podstawowe właściwości mechaniczne gumy w taki sposób, aby podać nie tylko ich definicje, ale przede wszystkim znaczenie i powiązanie z innymi właściwościami oraz skrótowo przedstawić ich odniesienie do składu mieszanki gumowej, jej przetwórstwa i zastosowania. Zdefiniowanie tych właściwości umożliwi w dalszych publikacjach z tej serii swobodne korzystanie z wprowadzonych tutaj pojęć.

EN

In this paper the fundamental mechanical properties of rubber are shown in such a way to give not only their definitions but first of all the meaning and the connection with other properties. Also the connection of the properties with composition of rubber compounds, their processing and applications are shortly presented. The definitions of the properties make possible freely use them in further publications of this series.

4

Investigation and analysis of periodic problem for layered composite structure on periodic foundation by means of non-smooth argument transformation method

Starushenko G., Krulik N., Tokarzewski S.

International Journal of Applied Mechanics and Engineering

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2003

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Vol. 8, no spec.

169-177

EN

The solution of the periodic problem for layered composite structure on the discretely located linear-elastic bearings has been obtained in the paper (Starushenko, 2000). The general case of the problem is considered in this paper. The structure that is located on the combined continuous and discrete elastic foundation is examined. The foundation rigidity is periodically changed in the composite phase limits. The structure is fortified by elastic supports in the component part junction. The problem is solved for general problem statement. It is supposed that physical and geometrical characteristics of the body and elastic foundation can accept any value. The periodic solution of the problem has been obtained in components of displacement function by means of saw-tooth argument transformation method in the paper. Analysis of obtained solution has been carried out. The flexure functions of the elastic foundation depending of the structure rigidity and geometric factors have been found.

5

Analysis of Optimality Conditions for Some Topology Optimization Problems in Elasticity

Trabucho L.

International Journal of Applied Mathematics and Computer Science

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2002

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Vol. 12, no 1

127-137

EN

The subject of topology optimization has undergone an enormous practical development since the appearance of the paper by Bends\o e and Kikuchi (1988), where some ideas from homogenization theory were put into practice. Since then, several engineering applications as well as different approaches have been developed successfully. However, it is difficult to find in the literature some analytical examples that might be used as a test in order to assess the validity of the solutions obtained with different algorithms. As a matter of fact, one is often faced with numerical instabilities requiring a fine tuning of the algorithm for each specific case. In this work, we develop a family of analytical solutions for very simple topology optimization problems, in the framework of elasticity theory, including bending and extension of rods, torsion problems as well as plane stress and plane strain elasticity problems. All of these problems are formulated in a simplified theoretical framework. A key issue in this type of problems is to be able to evaluate the sensitivity of the homogenized elastic coefficients with respect to the microstructure parameter(s). Since we are looking for analytical solutions, we use laminates for which an explicit dependence of the homogenized coefficients on the microstructure is known.

6

The influence of general surface loading on penetration of a circular punch into an elastic stratum

Rogowski B., Zaręba D.

Engineering Transactions

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1998

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Vol. 46, iss. 2

205-215

EN

The first of the authors (B.R.) derived an expression for the pressure distribution inside a circular region with vanishing shear tractions and normal displacements, due to the application of the forces distributed along the circumference on an elastic transversely isotropic half-space. This results is used to derive the relationships between the forces, moments and indentations for a punch acting on an elastic half-space. The results are given in terms of elementary functionss, The influence of an annular punch encircling a central punch is considered. The stress intensity factor of Mode I related to non-symmetric stress distribution in the vicinity of ann external crack under general surface loading, symmetric with respect to the crack plane, is also presented in terms of elementary functions.