Wyniki wyszukiwania - Biblioteka Nauki

1

Phase transitions in thermoelastic and thermoviscoelastic shells

100%

Eremeyev V. A. , Pietraszkiewicz W.

Archives of Mechanics

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2009

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tom Vol. 61, nr 1

41-67

EN

Applaying the general non-linear theory of shells undergoing phase transitions, we derive the balance equations along the singular surface curve modelling the phase interface in the shell. From the integral forms of balance laws of linear momentum, angular momentum, and energy as well as the entropy inequality, we obtain the local static balance equations along the curvilinear phase interface. We discuss general forms of the constitutive equations for thermoelastic and thennoviscoelastic shells, as well as propose their simple cases for the linear isotropic shell behaviour. We also derive the thermodynarnic condition allowing one to determine the interface position on the deformed shell miclsurface. The theoretical model is illustrated by the example of thin circular cylindrical shell made of a two-phase elastic material subjected to tensile forces at the shell boundary. The solution reveals the existence of the hysteresis loop whose size depends upon values of several loading parameters. Key words: non-linear shell, phase transition, kinetic equation, quasi-static loading, thermoviscoelasticity, extended cylinder.

2

On determination of displacements from given strains and height function in the non-linear theory of thin shells

100%

Szwabowicz M. L. , Pietraszkiewicz W.

Journal of Theoretical and Applied Mechanics

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2002

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tom Vol. 40 nr 1

259-272

EN

The position vector of the deformed shell reference surface is expressed by its projection onto the coordinate plane and the height function over that plane. The projected position is then determined by quadratures entirely from three surface strains and the height function. The latter fields can be found as solutions to the non-linear boundary value problem of thin elastic shells, developed by Szwabowicz (1999). The corresponding displacement field is determined from the deformed position vector by simple algebraic formulae.

PL

Wektor wodzący powierzchni podstawowej powłoki odkształconej wyrażono przez jego rzut na płaszczyznę odniesienia i funkcję wysokości ponad tę płaszczyznę. Zrzutowane składowe tego wektora wyznaczono za pomocą kwadratur zależnych od odkształceń powierzchni i funkcji wysokości, które można wyznaczyć, rozwiązując zagadnienie brzegowe nieliniowej teorii cienkich powłok sprężystych w postaci zaproponowanej przez Szwabowicza (1999). Odnośne pole przemieszczeń wyznaczono przy pomocy prostych wzorów algebraicznych.

3

Thermomechanics of Shells with Sigular Curves

100%

Makowski J. , Pietraszkiewicz W.

Zeszyty Naukowe Instytutu Maszyn Przepływowych Polskiej Akademii Nauk w Gdańsku

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2002

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tom nr 528/1487

1-100

EN

We formulate rigorously the global and local laws of mechanics and thermodynamics for shells with singularities at some stationary or moving curves in the shell base surface (itself not necessarily smooth). The laws are derived in an exact manner from underlying laws of continuum thermomechanics written in the integral - impulse form for the shell-like body. Our formulation is sufficiently general to include not only traditional applications to reversible problems of regular shells, but also those modeling irreversible and non-smooth processes in irregular shells. We assume that the shell-like body is represented in the physical space by the base surface' which in a reference configuration is only Lipschitz continuous with almost smooth boundary. By a moving singular curve we mean a one-parameter family of piecewise smooth surface curves which transverse the reference configuration of the shell base surface and across which various thermomechanical field variables may suffer jump discontinuities. However, all the fields are assumed to be regular enough for the generalized surface transport and gradient-divergence theorems to be applicable. As a result of complex transformations presented in the report, at regular points of the reference base surface and for almost all time instants we obtain five local laws of shell thermomechanics: the balance of mass, linear momentum, angular momentum, and energy as well as the entropy inequality. From the transformations we also obtain, corresponding to the laws of shell thermomechanics, five continuity conditions at regular points of every singular surface curve. Additionally, we discuss exact 2D shell kinematics and exact 2D shell strain measures. The principal features of the derived field equations and side conditions are: 1) the classical expressions for the linear and angular momenta are not assumed from the outset (they must be given by appropriate constitutive equations), 2) there is no classical splitting of the total energy into the sum of internal and kinetic energies (such a splitting is considered as a part of constitutive theory), 3) the entropy source and the entropy influx are not directly related to temperature, 4) there are two additional terms in the equation of energy balance which represent the interstitial working (they require a suitable constitutive prescription). We show that within the general shell thermomechanics the constitutive equations are needed for the surface stress tensor, the surface couple tensor, the specific total energy, the specific entropy, and the heat influx vector fields. But additionally we need the constitutive prescription for the linear and angular momenta vectors, as well as possibly for several other supplementary field variables. General expressions for the constitutive equations are given through response functionals of the histories of motion and temperature fields. For spatially first-grad "simple" shells we propose reduced forms of constitutive equations in the spatial and material representations. We also discuss additional constitutive assumptions which would allow us to eliminate temperatures, heats and entropy influxes at the upper and lower shell faces, as well as fields describing the interstitial working, the extra entropy source and the extra entropy flux. We derive the reduced dissipation inequality for shells and use it to develop thermodynamically consistent constitutive equations appropriate for heat conducting and thermo-visco-elastic shells. Particular forms of constitutive equations for thermoelastic, isothermal or higher-grad shells are proposed. By introducing thermodynamic potentials we also discuss constitutive nature of representing the total shell energy density as the sum of potential, kinetic and interstitial energy densities. Finally, we propose general and some specific forms of the kinetic constitutive equations for the linear and angular momenta. The results presented in this report may be considered as an introduction to a variety of thermomechanical problems of the regular and irregular shells, which might be formulated and solved already in the near future.

4

Non-linear dynamics of flexible shell structures

80%

Chróścielewski J. , Makowski J. , Pietraszkiewicz W.

Computer Assisted Mechanics and Engineering Sciences

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2002

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tom Vol. 9, No. 3

341-357

EN

The initial-boundary value problem in the weak form is formulated for the general six-field non-linear theory of branched shell structures. The extended time-stepping algorithm of the Newmark type is worked out for the non-linear dynamic analysis on the configuration space containing the rotation group SO(3). Within the finite element approximation, an accurate indirect C0 interpolation procedure on SO(3) with a transport of approximation domain is developed. Numerical simulations by the finite element method of 2D and 3D large overall motions of several flexible elastic shell structures are presented. It is shown that values of potential and kinetic energies may oscillate in time, but the total energy remains conserved during the free motion of the structures in space.

5

On the general form of jump conditions for thin irregular shells

80%

Makowski J. , Pietraszkiewicz W. , Stumpf H.

Archives of Mechanics

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1998

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tom Vol. 50, nr 3

483-495

EN

The paper deals with the nonlinear theory of thin shell structures in the presence of irregularities in geometry, deformation, material properties and loading. The irregular shell is modelled by a reference network being a union of piecewise smooth surfaces and space curves, with various fields satisfying relaxed smoothness, differentiability, and regularity requirements. Transforming the virtual work principle postulated for the entire reference network, the corresponding local field equations and side conditions (boundary and jump conditions) are derived. It is shown that no more than four static and work-conjugate kinematic jump conditions can correctly be formulated whenever the shell deformation is assumed to be entirely determined by deformation of the reference network capable of resisting to stretching and bending. This assumption includes various specjal formulations of the Kirchhoff-Love type theory of elastic shells, as well as their substantial generalizations accounting for finite strains and inelastic deformations.

6

The 10th Jubillee Conference „Shell Structures: Theory and Applications”, SSTA2013,Oct. 16-18, 2013, Gdańsk (Poland)

60%

Górski J. , Pietraszkiewicz W.

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