Stress intensity factors for interface crack in finite size specimen using a generalized variational approach

A generalized variational approach together with eigenfunction expansion is applied to determine the stress intensity factors for interface crack in finite size specimen. Application is also made of the complex potentials such that a complex stress intensity factor with components corresponding to the Mode I and II stress intensity factors can be identified with one of the leading coefficients in the eigenfunction expansion. Obtained are the numerical values of the stress intensity factors for an interface edge crack in a bimaterial rectangular specimen. The outside boundary is subjected to uniform stress normal and parallel to the crack. Solutions are also obtained for the same crack aand specimen geoinetry is subjected to a pair of equal and opposite concentrated forces along the open end away from the edge crack. The third example pertains to the case of three-point bending where the centre concentrated load is directed along the interface dividing the two materials. Numerical results are obtained for four different combinations of the bimaterial specimen with an interface edge crack.     

A modified variational approach for the analysis of piled raft foundation

A modified variational approach is presented to study the behavior of piled raft foundation under vertical loads. The free-body for analysis is a flexible raft isolated from piled raft foundation instead of pile group–soil system or whole pile raft system, which are usually used in other researches. The deflected shape of raft is represented by a function with a set of undetermined coefficients and the interactions between piles and/or the surface loads of soil are evaluated by a simplified approximate analytical solution. The response of the piled raft system is determined by the principle of minimum potential energy. Compared to other rigorous approaches, the present method is computationally efficient and inexpensive. The solutions obtained using the present method of analysis are shown to be in good agreement with other available published results.     

Second-order theory for the effective behavior and field fluctuations in viscoplastic polycrystals

A recently developed “second-order” homogenization procedure (Ponte Castañeda (J. Mech. Phys. Solids 50 (2002a, b) 737, 759)) is extended to viscoplastic polycrystals and applied to compute the effective response of a certain special class of isotropic polycrystals. The method itself reduces to a simple expression requiring the computation of the averages of the stress field and the covariances of its fluctuations over the various grain orientations in an optimally selected “linear comparison polycrystal”. Therefore, the method not only allows the determination of the effective behavior of the polycrystal, but as a byproduct also yields information on the heterogeneity of the stress and strain-rate fields within the polycrystal. An application is given for a model 2-dimensional, isotropic polycrystal with power-law behavior for the constituent grains. The resulting predictions for the effective behavior are found to satisfy sharp bounds available from the literature and to be consistent with the results of recent numerical simulations. The associated averages and fluctuations of the stresses and strain rates are found to depend strongly on the strain-rate sensitivity (i.e., nonlinearity) and grain anisotropy. In particular, the stress and strain-rate fluctuations were found to grow and become strongly anisotropic with increasing values of the nonlinearity and grain anisotropy parameters.     

Variational formulation of a rod under torsional vibration for crack identification

A variational formulation is developed for the torsional vibration of a cylindrical shaft with a circumferential crack. The work is compared with existing methods. The Hu–Washizu–Barr variational formulation was used to develop the differential equation and the boundary conditions of the cracked rod. The general variational principle and the independent assumptions about the displacement, the momentum, the strain and the stress fields of the cracked rod, and the equations of motion for a uniform rod in torsional vibration, are derived. The crack was modelled as a continuous flexibility using the displacement field in the vicinity of the crack, found with fracture mechanics methods. Rayleigh quotient was used to approximate the natural frequencies of the cracked rod. Independent evaluations of crack identification methods in rotating shafts are reported and compared with methods using the continuous crack flexibility theory.     

Two exact micromechanics-based nonlocal constitutive equations for random linear elastic composite materials

A Hashin-Shtrikman-Willis variational principle is employed to derive two exact micromechanics-based nonlocal constitutive equations relating ensemble averages of stress and strain for two-phase, and also many types of multi-phase, random linear elastic composite materials. By exact is meant that the constitutive equations employ the complete spatially-varying ensemble-average strain field, not gradient approximations to it as were employed in the previous, related work of Drugan and Willis (J. Mech. Phys. Solids 44 (1996) 497) and Drugan (J. Mech. Phys. Solids 48 (2000) 1359) (and in other, more phenomenological works). Thus, the nonlocal constitutive equations obtained here are valid for arbitrary ensemble-average strain fields, not restricted to slowly-varying ones as is the case for gradient-approximate nonlocal constitutive equations. One approach presented shows how to solve the integral equations arising from the variational principle directly and exactly, for a special, physically reasonable choice of the homogeneous comparison material. The resulting nonlocal constitutive equation is applicable to composites of arbitrary anisotropy, and arbitrary phase contrast and volume fraction. One exact nonlocal constitutive equation derived using this approach is valid for two-phase composites having any statistically uniform distribution of phases, accounting for up through two-point statistics and arbitrary phase shape. It is also shown that the same approach can be used to derive exact nonlocal constitutive equations for a large class of composites comprised of more than two phases, still permitting arbitrary elastic anisotropy. The second approach presented employs three-dimensional Fourier transforms, resulting in a nonlocal constitutive equation valid for arbitrary choices of the comparison modulus for isotropic composites. This approach is based on use of the general representation of an isotropic fourth-rank tensor function of a vector variable, and its inverse. The exact nonlocal constitutive equations derived from these two approaches are applied to some example cases, directly rationalizing some recently-obtained numerical simulation results and assessing the accuracy of previous results based on gradient-approximate nonlocal constitutive equations.     

Fundamental equations of certain electromagnetic-acoustic discontinuous fields in variational form

We present, in the first part of the paper, the well-known fundamental electromagnetic-acoustic equations, that is, the coupled Maxwells and Newtons equations for an elastic dielectric continuum in differential form, and we also discuss the uniqueness of their linear solutions. In the second part, from a general principle of physics, we deduce a three-field variational principle that operates on the mechanical displacements, the electric potential, and the electromagnetic vector potential of the dielectric continuum. Then, we extend it through an involutory (or Friedrichss) transformation in deriving a nine-field unified variational principle that operates on the mechanical, electrical, and magnetic continuous linear fields under the infinitesimal strains. This variational principle generates Maxwells and Newtons equations, the coupled linear constitutive relations, and the associated natural boundary conditions for the regular region of the dielectric continuum as its Euler-Lagrange equations. In the third part, we further generalise the unified variational principle so as to incorporate the jump conditions across a surface of discontinuity within the dielectric region. We also show that the integral and differential types of variational principles that apply to the linear motions of the elastic dielectric region with a fixed internal surface of discontinuity are in agreement with and recover, as special cases, some of the earlier variational principles. Further, the variational principles may be directly used in linear electromagnetic and/or acoustic field computations and in consistently establishing the lower order one- or two-dimensional equations of the elastic dielectric continuum.Received: 9 January 2002, Accepted: 26 May 2003, Published online: 5 December 2003PACS: 03.40, 41.10, 77.60 Correspondence to: G.A. Altay     

A Hybrid Viscosity Approximation Method for a Common Solution of a General System of Variational Inequalities,an Equilibrium Problem,and Fixed Point Problems

In this paper, we introduce a new iterative method based on the hybrid viscosity approximation method for finding a common element of the set of solutions of a general system of variational inequalities, an equilibrium problem, and the set of common fixed points of a countable family of nonexpansive mappings in a Hilbert space. We prove a strong convergence theorem of the proposed iterative scheme under some suitable conditions on the parameters. Furthermore, we apply our main result for W-mappings. Finally, we give two numerical results to show the consistency and accuracy of the scheme.     

RN中一类带Hardy-Sobolev临界指数项的Kirchhoff型问题的正解*

研究如下一类带Hardy-Sobolev临界指数的Kirchhoff型问题: 其中N ≥ 3, a, λ ≥ 0, b, m > 0, 0 ≤ s < 2, h ∈ L^2*/2*-1 (R^N )为非零非负函数.当λ = 0时, 利用分析技巧获得了问题可解性结果. 当λ > 0时, 利用变分方法获得该问题正解的存在性.特别地, 当0 < m < 2-s/N-2时, 获得了问题至少存在两个正解.     

Toward assessment of density functionals for vibronic coupling in two‐photon absorption: A case study of 4‐nitroaniline

In this study, we predict vibronic two‐photon absorption (TPA) spectra for 4‐nitroaniline in vacuo. The simulations are performed using density functional theory and the approximate second‐order coupled‐cluster singles and doubles model CC2. Thereby we also demonstrate the possibility of simulations of vibronic TPA spectra with ab initio wavefunction methods that include electron correlation for medium‐sized systems. A special focus is put on the geometric derivatives of the second‐order transition moment and the dipole moment difference between the charge‐transfer excited state and the ground state. The results of CC2 calculations bring new insight into the vibronic coupling mechanism in TPA spectra of 4‐nitroniline and demonstrate that the mixed term is quite large and that it also exhibits a negative interference with the Franck‐Condon contribution. © 2015 Wiley Periodicals, Inc.     

Review of validation and reporting of non-targeted fingerprinting approaches for food authentication

Food fingerprinting approaches are expected to become a very potent tool in authentication processes aiming at a comprehensive characterization of complex food matrices. By non-targeted spectrometric or spectroscopic chemical analysis with a subsequent (multivariate) statistical evaluation of acquired data, food matrices can be investigated in terms of their geographical origin, species variety or possible adulterations. Although many successful research projects have already demonstrated the feasibility of non-targeted fingerprinting approaches, their uptake and implementation into routine analysis and food surveillance is still limited. In many proof-of-principle studies, the prediction ability of only one data set was explored, measured within a limited period of time using one instrument within one laboratory. Thorough validation strategies that guarantee reliability of the respective data basis and that allow conclusion on the applicability of the respective approaches for its fit-for-purpose have not yet been proposed. Within this review, critical steps of the fingerprinting workflow were explored to develop a generic scheme for multivariate model validation. As a result, a proposed scheme for “good practice” shall guide users through validation and reporting of non-targeted fingerprinting results. Furthermore, food fingerprinting studies were selected by a systematic search approach and reviewed with regard to (a) transparency of data processing and (b) validity of study results. Subsequently, the studies were inspected for measures of statistical model validation, analytical method validation and quality assurance measures. In this context, issues and recommendations were found that might be considered as an actual starting point for developing validation standards of non-targeted metabolomics approaches for food authentication in the future. Hence, this review intends to contribute to the harmonization and standardization of food fingerprinting, both required as a prior condition for the authentication of food in routine analysis and official control.