ISSN:0044-2267    

DOI:10.1002/zamm.19970770502

出版商:WILEY‐VCH Verlag    

年代:1997

数据来源: WILEY

ISSN:0044-2267    

DOI:10.1002/zamm.19970770503

出版商:WILEY‐VCH Verlag    

年代:1997

数据来源: WILEY

摘要:

AbstractSome properties of the tensor algebra on manifolds are discussed with respect to the classical tensor algebra of continuum mechanics. Basic definitions and relations of linear maps are briefly recalled and applied to tensor spaces, where special attention is focused to the definition of dual and transposed maps. As application to nonlinear continuum mechanics, algebraic pull‐back and push‐forward maps, and Lie‐like time derivatives associated with linear maps are defined and used to build up commutative schemes for deformation measures, objective deformation rates, stresses, and frame‐invariant forms of the stress power. The transition to the classical formulation of tensor algebra by identifying vector spaces and their duals is examined. It is shown how this concept enables a straight‐forward derivation of the Doyle‐Ericksen formula and its possib

ISSN:0044-2267    

DOI:10.1002/zamm.19970770504

出版商:WILEY‐VCH Verlag    

年代:1997

数据来源: WILEY

ISSN:0044-2267    

DOI:10.1002/zamm.19970770507

出版商:WILEY‐VCH Verlag    

年代:1997

数据来源: WILEY

摘要:

AbstractFirst the observation levels for materials are discussed. Then a material is modelled as a heterogeneous continuum consisting of grains, each of them being a tiny continuum in its turn. As demonstration material steel consisting of two phases is selected. In the case of duplex steel the material consists a priori of two phases at fixed volume fractions. Subsequently, the martensitic transformation in a Fe‐Ni steel is investigated as an example for a material with changing volume fractions of the phases. It is shown how continuum mechanics and thermodynamics can help to explain the some‐what unexpected deformation behavior of those materials.Vorerst werden die verschiedenen Beobachtungsmaßstäbe für Werkstoffe erörtert. In der Folge wird ein Werkstoff als heterogenes Kontinuum im Sinne einer Ansammlung von Körnern betrachtet. Jedes Korn für sich stellt wiederum ein kleines Kontinuum dar. Als Demonstrationsmaterial wird Stahl ausgewählt, der aus zwei Phasen besteht. Im Falle des Duplexstahles besitzt das Material zwei Phasen mit fixer Volumsfraktion. Weiters wird die martensitische Umwandlung in einem Fe‐Ni‐Stahl behandelt, die zu einer veränderlichen Volumsfraktion der beiden Phasen führt. Es wird gezeigt, wie die Kontinuumsmechanik und Thermodynamik beitragen können, um das doch merkwürdige Verformungsverhalten dieser beiden Werk

ISSN:0044-2267    

DOI:10.1002/zamm.19970770508

出版商:WILEY‐VCH Verlag    

年代:1997

数据来源: WILEY

摘要:

AbstractIn this paper a general procedure for a rational derivation of plate theories is proposed. The methodology is based on the conjecture that plate theories can be carried out from the three‐dimensional elasticity by imposing suitable constraints on the strain and stress fields. The powerful Lagrange multipliers theory is adopted to derive the variational principles, based on the Hu‐Washizu functional, governing the constrained elasticity problems. Both the first‐order shear deformation plate theory, and the higher‐order Lo‐Christensen‐Wu plate theory are derived. The governing equations are recovered, and the reactive fields, arising as a consequence of the imposed constraints, are carried out. When these reactive fields are taken into account, the equilibrium, congruence, and constitutive equations turn out to be exactl

ISSN:0044-2267    

DOI:10.1002/zamm.19970770509

出版商:WILEY‐VCH Verlag    

年代:1997

数据来源: WILEY

摘要:

AbstractWe consider a mathematical model of the fluid indicated in the title which is useful in describing several processes of industrial interest like gas flow in lighting devices or flow of molt glass in a glass furnace. This model includes the three‐dimensional Navier‐Stokes equations, mass conservation, and equations for radiation intensity (differential approximation) and temperature.The problem is rewritten to define a weak solution the existence of which we re‐prove following a paper by J. Förste. For unicity of the solution we give a modified proof (under suitable conditions on the solution d

ISSN:0044-2267    

DOI:10.1002/zamm.19970770510

出版商:WILEY‐VCH Verlag    

年代:1997

数据来源: WILEY

ISSN:0044-2267    

DOI:10.1002/zamm.19970770512

出版商:WILEY‐VCH Verlag    

年代:1997

数据来源: WILEY

摘要:

AbstractSeveral optimal design problems with a variational inequality with a monotone operator as common state problem are considered. The inequality represents the bending of a Reissner‐Mindlin plate, resting on a unilateral elastic foundation and on some unilateral rigid piers. Both the thickness of the plate and the stiffness of the foundation play the role of design variables. The cost functionals include the intensity of shear stresses, and reactive forces on the piers or the weight of the plate. The solvability of all the problems is prove

ISSN:0044-2267    

DOI:10.1002/zamm.19970770513

出版商:WILEY‐VCH Verlag    

年代:1997

数据来源: WILEY

ISSN:0044-2267    

DOI:10.1002/zamm.19970770516

出版商:WILEY‐VCH Verlag    

年代:1997

数据来源: WILEY