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Energy Principle (energy + principle)
Selected AbstractsExtension of the Griffith's fracture criteria to saturated claysINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 4 2003K.M. Dégué Abstract Inglis [1] has solved the problem of distribution of stress in an elastic plate around an elliptical hole. His works clarify the role of cracks in the failure of an elastic material. However, his solution cannot be applied to saturated clay because he considers only total stresses, while, in saturated clay, the criterion of rupture should be expressed in terms of effective and not total stresses. The solution of Atkinson and Craster [2] using Biot's poroelasticity theory, shows that there is no high pore pressure in the vicinity of the crack tips for saturated clay. The major difference between this approach and the Biot's theory of is that, in saturated clay, strain is a function of the variation of the effective stress [3], while, in poroelastic media, strain is only a function of the variation of the total stress [4, Equation 2.2]. Also in their solution there is continuity between the pore fluid and the inner fluid in the crack. Their solution is valid for poroelastic media involving a movement of the pore fluid. In our solution there is no movement of the pore fluid (Undrained condition). In this paper we have solved the same problem as Inglis [1], but for the particular case of saturated clay obeying elastic law. By solving this problem we obtained the expressions for pore pressure, effective stress, total stress and displacements. The results show that not only the total stress but also the pore pressure and the effective stress are also high in the vicinity of the crack tips. A new failure criterion, based on Griffith's strain energy principle [5] and maximum tensile stress [6], valid for saturated clay is developed in this paper. Copyright © 2003 John Wiley & Sons, Ltd. [source] An a posteriori error estimator for the p - and hp -versions of the finite element methodINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 1 2005J. E. Tarancón Abstract An a posteriori error estimator is proposed in this paper for the p - and hp -versions of the finite element method in two-dimensional linear elastostatic problems. The local error estimator consists in an enhancement of an error indicator proposed by Bertóti and Szabó (Int. J. Numer. Meth. Engng. 1998; 42:561,587), which is based on the minimum complementary energy principle. In order to obtain the local error estimate, this error indicator is corrected by a factor which depends only on the polynomial degree of the element. The proposed error estimator shows a good effectivity index in meshes with uniform and non-uniform polynomial distributions, especially when the global error is estimated. Furthermore, the local error estimator is reliable enough to guide p - and hp -adaptive refinement strategies. Copyright © 2004 John Wiley & Sons, Ltd. [source] Toroidal magnetic fields in type II superconducting neutron starsMONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY, Issue 4 2008T. Akgün ABSTRACT We determine constraints on the form of axisymmetric toroidal magnetic fields dictated by hydrostatic balance in a type II superconducting neutron star with a barotropic equation of state. Using Lagrangian perturbation theory, we find the quadrupolar distortions due to such fields for various models of neutron stars with type II superconducting and normal regions. We find that the star becomes prolate and can be sufficiently distorted to display precession with a period of the order of years. We also study the stability of such fields using an energy principle, which allows us to extend the stability criteria established by R. J. Tayler for normal conductors to more general media with magnetic free energy that depends on density and magnetic induction, such as type II superconductors. We also derive the growth rate and instability conditions for a specific instability of type II superconductors, first discussed by P. Muzikar, C. J. Pethick and P. H. Roberts, using a local analysis based on perturbations around a uniform background. [source] Crustal Composition of China Continent Constrained from Heat Flow Data and Helium Isotope Ratio of Underground FluidACTA GEOLOGICA SINICA (ENGLISH EDITION), Issue 1 2010Yang WANG Abstract: Based on conservation of energy principle and heat flow data in China continent, the upper limit of 1.3 ,W/m3 heat production is obtained for continental crust in China. Furthermore, using the data of heat flow and helium isotope ratio of underground fluid, the heat productions of different tectonic units in China continent are estimated in range of 0.58,1.12 ,W/m3 with a median of 0.85 ,W/m3. Accordingly, the contents of U, Th and K2O in China crust are in ranges of 0.83,1.76 ,g/g, 3.16,6.69 ,g/g, and 1.0%,2.12%, respectively. These results indicate that the abundance of radioactive elements in the crust of China continent is much higher than that of Archean crust; and this fact implies China's continental crust is much evolved in chemical composition. Meanwhile, significant lateral variation of crustal composition is also exhibited among different tectonic units in China continent. The crust of eastern China is much enriched in incompatible elements such as U, Th and K than that of western China; and the crust of orogenic belts is more enriched than that of platform regions. It can also be inferred that the crusts of eastern China and orogenic belts are much felsic than those of western China and platform regions, respectively, derived from the positive correlation between the heat production and SiO2 content of bulk crust. This deduction is consistent with the results derived from the crustal seismic velocity data in China. According to the facts of the lower seismic velocity of China than the average value of global crust, and the higher heat production of China continent compared with global crust composition models published by previous studies, it is deduced that the average composition models of global continent crust by Rudnick and Fountain (1995), Rudnick and Gao (2003), Weaver and Tarney (1984), Shaw et al. (1986), and Wedepohl (1995) overestimate the abundance of incompatible elements such as U, Th and K of continental crust. [source] Lower and upper bound estimation of isotropic and orthotropic fracture mechanics problems using elements with rotational degrees of freedomINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 5 2008Antoinette de Klerk Abstract We use Rice's path-independent J integral, as well as its dual, the I* integral, to estimate lower and upper bounds of the stress intensity factor K in linear elastic fracture mechanics problems. The elements used contain rotational degrees of freedom, and are derived from the correct energy principles to guarantee path independence of the integrals. That is, the displacement-based elements used in calculating the J integral are derived from the principle of potential energy; the assumed stress elements used in calculating the I* integral are derived from complementary energy principles. For lower bound estimation in particular, elements with drilling degrees of freedom are advantageous, due to their superior accuracy. Numerical results are presented for isotropic and orthotropic mode I and mode II fracture mechanics problems. In addition, we reflect on suitable finite element integration schemes, and applicable values for the problem dependent penalty parameter , which is used in deriving the elements. Copyright © 2006 John Wiley & Sons, Ltd. [source] | ||||||||||