The Experts below are selected from a list of 36 Experts worldwide ranked by ideXlab platform
C G Panagiotopoulos - One of the best experts on this subject based on the ideXlab platform.
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Velocity-based Boundary Integral EquationFormulation In The Time Domain
Mesh Reduction Methods, 2009Co-Authors: G. D. Manolis, C G PanagiotopoulosAbstract:In this work, we present a Reciprocal theorem of linear elastodynamics derived in terms of velocities instead of displacements, which seems to be better suited in relating two different elastodynamic states of an elastic region for several reasons that will be discussed latter on. As with the conventional displacement integral equation representation, using this alternative Reciprocal theorem we can produce a velocity integral equation representation and then formulate a novel numerical approximation based on the boundary element method (BEM). Furthermore, a thorough stability performance analysis of the formulations arise utilizing displacement and/or velocity Reciprocal Theorems is presented.
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Reciprocal Theorems in structural dynamics including initial conditions
Earthquake Engineering & Structural Dynamics, 2006Co-Authors: C G PanagiotopoulosAbstract:For completeness purposes, as well as for practical reasons, this work investigates the well-known Betti–Rayleigh Reciprocal theorem for structural dynamics in a way which includes the effect of initial conditions. It then presents a natural and consistent way for introducing the Duhamel integral for the transient response of a dynamical system through the aforementioned Reciprocal theorem. Copyright © 2005 John Wiley & Sons, Ltd.
Magdy A Ezzat - One of the best experts on this subject based on the ideXlab platform.
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convolutional variational principle Reciprocal and uniqueness Theorems in linear fractional two temperature thermoelasticity
Journal of Thermal Stresses, 2011Co-Authors: A El S Karamany, Magdy A EzzatAbstract:Two general models of fractional heat conduction law for non-homogeneous anisotropic elastic solid is introduced and the constitutive equations for the two-temperature fractional thermoelasticity theory are obtained, uniqueness and Reciprocal Theorems are proved and the convolutional variational principle is established and used to prove a uniqueness theorem with no restrictions imposed on the elasticity or thermal conductivity tensors except symmetry conditions. The two-temperature dynamic coupled, Lord-Shulman and fractional coupled thermoelasticity theories result as limit cases. The reciprocity relation in case of quiescent initial state is found to be independent of the order of differintegration.
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uniqueness and Reciprocal Theorems in linear micropolar electro magnetic thermoelasticity with two relaxation times
Mechanics of Time-dependent Materials, 2009Co-Authors: Ahmed S Elkaramany, Magdy A EzzatAbstract:A general model for the linear micropolar electro-magnetic thermoelastic continuum based on the hyperbolic heat equation, which is physically more relevant than the classical thermoelasticity theory in analyzing problems involving very short intervals of time and/or very high heat fluxes, is introduced. An integral identity that involves two admissible processes at different instants is established. Uniqueness theorem is proved, with no definiteness assumption on the elastic constitutive coefficients and no restrictions on the electro-elastic coupling moduli, magneto-elastic coupling moduli, and thermal coupling coefficients other than symmetry conditions. The reciprocity theorem is derived, without the use of Laplace transforms. The integral representation formula is obtained in case instantaneous concentrated, time-continuous or time-harmonic loads are applied. The Maysel’s, Somigliana’s and Green’s formulas are derived. The mixed boundary value problem is considered and a system of five singular Fredholm integral equations is obtained. The results for dynamic classical coupled theory can be easy deduced from the given general model formulated for the temperature-rate dependent thermoelasticity.
G Falsone - One of the best experts on this subject based on the ideXlab platform.
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a complete set of corollaries of the Reciprocal Theorems in elasticity
International Journal of Solids and Structures, 1996Co-Authors: F Guarracino, V Minutolo, L Nunziante, G FalsoneAbstract:This work presents a complete set of corollaries derived from the classical Reciprocal Theorems in the linear theory of elasticity. It is shown that the strain energy required to produce a given effect (reactive generalised force or displacement) at a certain position A of a linearly elastic body or structure by means of the application of the corresponding dual action (imposed generalised displacement or force, respectively) at another position B, attains its minimum when A coincides with B. This fact turns out to be a simple and general property of any linearly elastic model and from a qualitative point of view it can be related to the well-known local perturbation principle of Boussinesq. The assertions made can prove themselves useful in the interpretation of terms arising in several engineering problems, like boundary elements analyses or structural monitoring procedures.
G. D. Manolis - One of the best experts on this subject based on the ideXlab platform.
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Velocity-based Reciprocal Theorems in elastodynamics and BIEM implementation issues
Archive of Applied Mechanics, 2010Co-Authors: Christos G. Panagiotopoulos, G. D. ManolisAbstract:Reciprocal Theorems in elastodynamics are introduced as extensions of respective Theorems from elastostatics. Inasmuch as the latter is a subset of the former, the aim here is to present an elastodynamic Reciprocal theorem that also includes elastostatics as a special case when the time variable becomes irrelevant. This is accomplished by introducing a velocity-based Reciprocal theorem, whose basic properties are subsequently explored. The next step is to use this theorem and formulate a numerical approach based on boundary integral equation statements and compare them with existing formulations based on conventional reciprocity relations. The applications presented here involve the standard mechanical oscillator and the unidimensional axial element as two simple, yet important problems of structural dynamics. Along with the numerical results, a thorough stability analysis of the corresponding time-stepping algorithms is formulated. In both cases, the superior performance of the methodologies built on velocity-based Reciprocal Theorems is clearly demonstrated.
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Velocity-based Boundary Integral EquationFormulation In The Time Domain
Mesh Reduction Methods, 2009Co-Authors: G. D. Manolis, C G PanagiotopoulosAbstract:In this work, we present a Reciprocal theorem of linear elastodynamics derived in terms of velocities instead of displacements, which seems to be better suited in relating two different elastodynamic states of an elastic region for several reasons that will be discussed latter on. As with the conventional displacement integral equation representation, using this alternative Reciprocal theorem we can produce a velocity integral equation representation and then formulate a novel numerical approximation based on the boundary element method (BEM). Furthermore, a thorough stability performance analysis of the formulations arise utilizing displacement and/or velocity Reciprocal Theorems is presented.
F Guarracino - One of the best experts on this subject based on the ideXlab platform.
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a complete set of corollaries of the Reciprocal Theorems in elasticity
International Journal of Solids and Structures, 1996Co-Authors: F Guarracino, V Minutolo, L Nunziante, G FalsoneAbstract:This work presents a complete set of corollaries derived from the classical Reciprocal Theorems in the linear theory of elasticity. It is shown that the strain energy required to produce a given effect (reactive generalised force or displacement) at a certain position A of a linearly elastic body or structure by means of the application of the corresponding dual action (imposed generalised displacement or force, respectively) at another position B, attains its minimum when A coincides with B. This fact turns out to be a simple and general property of any linearly elastic model and from a qualitative point of view it can be related to the well-known local perturbation principle of Boussinesq. The assertions made can prove themselves useful in the interpretation of terms arising in several engineering problems, like boundary elements analyses or structural monitoring procedures.