Home About us Contact
|
Home About us Contact | ||
|
|
||
Energy Functional (energy + functional)
Selected AbstractsA triangular plate element for thermo-elastic analysis of sandwich panels with a functionally graded coreINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 9 2006M. Das Abstract A sandwich construction is commonly composed of a single soft isotropic core with relatively stiff orthotropic face sheets. The stiffness of the core may be functionally graded through the thickness in order to reduce the interfacial shear stresses. In analysing sandwich panels with a functionally gradient core, the three-dimensional conventional finite elements or elements based on the layerwise (zig-zag) theory can be used. Although these elements accurately model a sandwich panel, they are computationally costly when the core is modelled as composed of several layers due to its grading material properties. An alternative to these elements is an element based on a single-layer plate theory in which the weighted-average field variablescapture the panel deformation in the thickness direction. This study presents a new triangular finite element based on {3,2}-order single-layer theory for modelling thick sandwich panels with or without a functionally graded core subjected to thermo-mechanical loading. A hybrid energy functional is employed in the derivation of the element because of a C1 interelement continuity requirement. The variations of temperature and distributed loading acting on the top and bottom surfaces are non-uniform. The temperature also varies arbitrarily through the thickness. Copyright © 2006 John Wiley & Sons, Ltd. [source] A variational r -adaption and shape-optimization method for finite-deformation elasticityINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 1 2004P. Thoutireddy Abstract This paper is concerned with the formulation of a variational r -adaption method for finite-deformation elastostatic problems. The distinguishing characteristic of the method is that the variational principle simultaneously supplies the solution, the optimal mesh and, in problems of shape optimization, the equilibrium shapes of the system. This is accomplished by minimizing the energy functional with respect to the nodal field values as well as with respect to the triangulation of the domain of analysis. Energy minimization with respect to the referential nodal positions has the effect of equilibrating the energetic or configurational forces acting on the nodes. We derive general expressions for the configurational forces for isoparametric elements and non-linear, possibly anisotropic, materials under general loading. We illustrate the versatility and convergence characteristics of the method by way of selected numerical tests and applications, including the problem of a semi-infinite crack in linear and non-linear elastic bodies; and the optimization of the shape of elastic inclusions. Copyright © 2004 John Wiley & Sons, Ltd. [source] The Pauli potential from the differential virial theoremINTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, Issue 12 2010Á. Nagy Abstract Recently, a first-order differential equation for the functional derivative of the kinetic energy functional is derived for spherically symmetric systems using the differential virial theorem of Nagy and March. Here, a more general first-order differential equation for the Pauli potential (valid not only for spherically symmetric systems) is derived by applying the differential virial theorem of Holas and March. The solution of the equation can be given by quantities capable of fully determining every property of a Coulomb system. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2010 [source] Interesting properties of Thomas,Fermi kinetic and Parr electron,electron-repulsion DFT energy functional generated compact one-electron density approximation for ground-state electronic energy of molecular systemsJOURNAL OF COMPUTATIONAL CHEMISTRY, Issue 9 2009Sandor Kristyan Abstract The reduction of the electronic Schrodinger equation or its calculating algorithm from 4N -dimensions to a (nonlinear, approximate) density functional of three spatial dimension one-electron density for an N -electron system, which is tractable in the practice, is a long desired goal in electronic structure calculation. If the Thomas-Fermi kinetic energy (,,,5/3dr1) and Parr electron,electron repulsion energy (,,,4/3dr1) main-term functionals are accepted, and they should, the later described, compact one-electron density approximation for calculating ground state electronic energy from the 2nd Hohenberg,Kohn theorem is also noticeable, because it is a certain consequence of the aforementioned two basic functionals. Its two parameters have been fitted to neutral and ionic atoms, which are transferable to molecules when one uses it for estimating ground-state electronic energy. The convergence is proportional to the number of nuclei (M) needing low disc space usage and numerical integration. Its properties are discussed and compared with known ab initio methods, and for energy differences (here atomic ionization potentials) it is comparable or sometimes gives better result than those. It does not reach the chemical accuracy for total electronic energy, but beside its amusing simplicity, it is interesting in theoretical point of view, and can serve as generator function for more accurate one-electron density models. © 2008 Wiley Periodicals, Inc. J Comput Chem 2009 [source] A relaxed model and its homogenization for nematic liquid crystals in composite materialsMATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 10 2004Quan Shen Abstract We analyse a model for equilibrium configurations of composite systems of nematic liquid crystal with polymer inclusions, in the presence of an external magnetic field. We assume that the system has a periodic structure, and consider the relaxed problem on the unit length constraint of the nematic director field. The relaxation of the Oseen,Frank energy functional is carried out by including bulk as well as surface energy penalty terms, rendering the problem fully non-linear. We employ two-scale convergence methods to obtain effective configurations of the system, as the size of the polymeric inclusions tends to zero. We discuss the minimizers of the effective energies for, both, the constrained as well as the unconstrained models. Copyright © 2004 John Wiley & Sons, Ltd. [source] Optical spectra of bismuth sulfochloride crystalsPHYSICA STATUS SOLIDI (B) BASIC SOLID STATE PHYSICS, Issue 1 2010A. Audzijonis Abstract We present the results of the ab initio theoretical study of the optical properties for paraelectric BiSCl crystal using the full potential linearized augmented plane wave (FP-LAPW) method as implanted in the Wien 2k code. For theoretical calculations of optical constants and functions we used the generalized gradient approximation (PBE-GGA), an improvement of the local spin-density approximation (LSDA) and recently Wu,Cohen (WC) proposed a new WC-GGA exchange-correlation energy functional. The dielectric function, refractive index, extinction coefficient, absorption coefficient, reflectivity, and energy loss function were calculated. The optical properties are analyzed and the origins of the peaks in the spectra are discussed in terms of the calculated density of states. [source] Ginzburg,Landau equations and boundary conditions for superconductors in static magnetic fieldsANNALEN DER PHYSIK, Issue 5 2005J. Bünemann Abstract We derive the Ginzburg,Landau equations for superconductors in static magnetic fields. Instead of the square of the gauge-invariant gradient of the order-parameter wave function, we consider the quantum-mechanical expression for the kinetic energy in the Ginzburg,Landau energy functional. We introduce a new surface term in the free energy functional which results in the de Gennes interface conditions. The phenomenological Ginzburg,Landau theory thus contains three length scales which must be determined from microscopic theory: the Ginzburg,Landau coherence length, the London penetration depth, and the de Gennes length. [source] Vortex energy and 360° Néel walls in thin-film micromagneticsCOMMUNICATIONS ON PURE & APPLIED MATHEMATICS, Issue 12 2010Radu Ignat We study the vortex pattern in ultrathin ferromagnetic films of circular crosssection. The model is based on the following energy functional: for in-plane magnetizations m: B2 , S1 in the unit disc . The avoidance of volume charges , · m , 0 in B2 and surface charges m · , , 0 on ,B2 leads to the formation of a vortex in the limit , , 0. At the level , > 0 the vortex is regularized by the formation of a 360° Néel wall (a one-dimensional transition layer with core of scale ,) concentrated along a radius of B2. We derive the limiting energy of the vortex by matching upper and lower bounds. Our analysis on the lower bound is based on a dynamical system argument and an interpolation inequality with sharp leading-order constant, while the upper bound uses the leading-order energy for 360° Néel walls. © 2010 Wiley Periodicals, Inc. [source] Action minimization and sharp-interface limits for the stochastic Allen-Cahn equationCOMMUNICATIONS ON PURE & APPLIED MATHEMATICS, Issue 3 2007Robert V. Kohn We study the action minimization problem that is formally associated to phase transformation in the stochastically perturbed Allen-Cahn equation. The sharp-interface limit is related to (but different from) the sharp-interface limits of the related energy functional and deterministic gradient flows. In the sharp-interface limit of the action minimization problem, we find distinct "most likely switching pathways," depending on the relative costs of nucleation and propagation of interfaces. This competition is captured by the limit of the action functional, which we derive formally and propose as the natural candidate for the ,-limit. Guided by the reduced functional, we prove upper and lower bounds for the minimal action that agree on the level of scaling. © 2006 Wiley Periodicals, Inc. [source] Analysis of microstructure development in shearbands by energy relaxation of incremental stress potentials: Large-strain theory for standard dissipative solidsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 1 2003Christian Miehe Abstract We propose a fundamentally new approach to the treatment of shearband localizations in strain softening elastic,plastic solids at finite strains based on energy minimization principles associated with microstructure developments. The point of departure is a general internal variable formulation that determines the finite inelastic response as a standard dissipative medium. Consistent with this type of inelasticity we consider an incremental variational formulation of the local constitutive response where a quasi-hyperelastic stress potential is obtained from a local constitutive minimization problem with respect to the internal variables. The existence of this variational formulation allows the definition of the material stability of an inelastic solid based on weak convexity conditions of the incremental stress potential in analogy to treatments of finite elasticity. Furthermore, localization phenomena are interpreted as microstructure developments on multiple scales associated with non-convex incremental stress potentials in analogy to elastic phase decomposition problems. These microstructures can be resolved by the relaxation of non-convex energy functionals based on a convexification of the stress potential. The relaxed problem provides a well-posed formulation for a mesh-objective analysis of localizations as close as possible to the non-convex original problem. Based on an approximated rank-one convexification of the incremental stress potential we develop a computational two-scale procedure for a mesh-objective treatment of localization problems at finite strains. It constitutes a local minimization problem for a relaxed incremental stress potential with just one scalar variable representing the intensity of the microshearing of a rank-one laminate aligned to the shear band. This problem is sufficiently robust with regard to applications to large-scale inhomogeneous deformation processes of elastic,plastic solids. The performance of the proposed energy relaxation method is demonstrated for a representative set of numerical simulations of straight and curved shear bands which report on the mesh independence of the results. Copyright © 2003 John Wiley & Sons, Ltd. [source] Infima of universal energy functionals on homotopy classesMATHEMATISCHE NACHRICHTEN, Issue 15 2006Stefan Bechtluft-Sachs Abstract We consider the infima (f) on homotopy classes of energy functionals E defined on smooth maps f: Mn , Vk between compact connected Riemannian manifolds. If M contains a sub-manifold L of codimension greater than the degree of E then (f) is determined by the homotopy class of the restriction of f to M \ L. Conversely if the infimum on a homotopy class of a functional of at least conformal degree vanishes then the map is trivial in homology of high degrees. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] | ||||||||||||||||