Thermal Analysis of Free‐Corner Effects in Cross‐Ply Plates by a Higher‐Order Theory Approach

Stresses in the vicinity of free edges and corners of composite laminates exhibit a distinct localized three‐dimensional behaviour [1] and thus represent an important technical situation. Since numerical analyses of stress concentration phenomena in layered structures are computationally expensive, the present contribution is devoted to a simple closed‐form higher‐order theory approach for the calculation of displacements, strains and stresses in the vicinity of a rectangular corner of symmetric cross‐ply laminates under uniform thermal load ΔT. An appropriate representation for the displacement field in the form of a single‐layer theory with unknown inplane components and appropriately assumed functions through the plate thickness yields closed‐form expressions for the strains and stresses throughout the whole laminate. Equilibrium and boundary conditions are fulfilled in an integral sense. The present approach is easily applied, is of a completely closed‐form analytic nature and requires only little computational effort. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Dynamic Shear Model for Layered Plates

A variant of a geometrically nonlinear dynamic shear model for layered plates is offered, where the inertial forces are taken into account at the stage of formation of hypotheses. A closed-form solution to the problem of forced vibrations is obtained for layered plates clamped or hinge-supported on their contour. The amplitude-frequency characteristics for various kinds of external loads are constructed. The influence of layer distribution across the package thickness is analyzed.     

A Class of 3D Problems for Layered Plates

Mechanics of Composite Materials - A class of 3D problems of elasticity theory for a layered package of orthotropic plates, which, in particular, models the behavior of the lithospheric plates of...     

开孔簿板非线性分析的数学模型和广义变分原理*

基于薄板非线性弯曲的Kirchhoff-Kármán假设.本文提出了在任意中面边界条件下任意开孔薄板非线性分析的三类边值问题并建立了相应的广义变分原理.能够看到在本文中提出的数学模型完全是一种新的不同于Karman理论的模型.这些数学模型能够应用于任意中面边界条件下开孔薄板的非线性分析和稳定性分析.     

A Variational Model for Dislocations at Semi-coherent Interfaces

We propose and analyze a simple variational model for dislocations at semi-coherent interfaces. The energy functional describes the competition between two terms: a surface energy induced by dislocations and a bulk elastic energy, spent to decrease the amount of dislocations needed to compensate the lattice misfit. We prove that, for minimizers, the former scales like the surface area of the interface, the latter like its diameter. The proposed continuum model is built on some explicit computations done in the framework of the semi-discrete theory of dislocations. Even if we deal with finite elasticity, linearized elasticity naturally emerges in our analysis since the far-field strain vanishes as the interface size increases.     

A New Hybrid Generalized Proximal Point Algorithm for Variational Inequality Problems

In this paper, we propose a modified Bregman-function-based proximal point algorithm for solving variational inequality problems. The algorithm adopts a similar constructive approximate criterion as the one developed by Solodov and Svaiter (Set Valued Analysis 7 (1999) 323) for solving the classical proximal subproblems. Under some suitable conditions, we can get an approximate solution satisfying the accuracy criterion via a single Newton-type step. We obtain the Fejér monotonicity to solutions of VIP for paramonotone operators. Some preliminary computational results are also reported to illustrate the method.     

Convergence of Hybrid Steepest-Descent Methods for Variational Inequalities

Assume that F is a nonlinear operator on a real Hilbert space H which is -strongly monotone and -Lipschitzian on a nonempty closed convex subset C of H. Assume also that C is the intersection of the fixed point sets of a finite number of nonexpansive mappings on H. We devise an iterative algorithm which generates a sequence (x _n ) from an arbitrary initial point x ₀H. The sequence (x _n ) is shown to converge in norm to the unique solution u* of the variational inequality

Convergence Analysis of Modified Hybrid Steepest-Descent Methods with Variable Parameters for Variational Inequalities

Assume that F is a nonlinear operator on a real Hilbert space H which is η-strongly monotone and κ-Lipschitzian on a nonempty closed convex subset C of H. Assume also that C is the intersection of the fixed-point sets of a finite number of nonexpansive mappings on H. We construct an iterative algorithm with variable parameters which generates a sequence {x _n } from an arbitrary initial point x ₀ ∊ H. The sequence {x _n } is shown to converge in norm to the unique solution u ^∗ of the variational inequality The authors thank the referees for helpful comments and suggestions His research was partially supported by the Teaching and Research Award Fund for Outstanding Young Teachers in Higher Education Institutions of MOE, China and the Dawn Program Foundation in Shanghai His research was partially supported by grant from the National Science Council of Taiwan His research was partially supported by grant from the National Science Council of Taiwan     

A Generalized Nonclassical Model of Stress-Strain State in the Problems of Statics,Dynamics, and Contact Interaction of Layered Plates and Shells

A new generalized two-dimensional nonclassical model for the dynamic stress-strain state of layered anisotropic plates and shallow shells is constructed. A feature of the model is the complete account of the factors which represent the spatial character of their deformation; in particular, the transverse shear and transverse compression strains as well as the geometrical nonlinearity and dynamic action of the load are accounted for.     

Variational Analysis for the Consumer Theory

We look for an interpretation of the demand correspondence in the consumer theory as a generalized derivative of the inverse utility function. We test the main concepts of nonsmooth analysis for such an objective. The proofs only use classical methods in optimization such as penalization and optimality conditions.     

A Comparison of Closed-Form and Finite-Element Solutions for the Free Vibration of Hybrid Cross-Ply Laminated Plates

Mechanics of Composite Materials - The natural frequencies of hybrid cross-ply laminated plates are predicted using a high-order shear deformation theory and the three-dimensional finite-element...     

A Hybrid Logistic Model for Case-Control Studies

For logistic regression in case-control studies, when risk factors associated with the outcome are exceedingly rare in the control group, the estimation of parameters in the model becomes difficult. In this paper, we propose a two-stage hybrid method to achieve this. In the first stage, we model the risk due to the rare factor, and in the second stage we model the residual risk due to the other factors using standard logistic model.     

基于双分数阶变分光流模型的运动目标检测方法

变分光流法是常用的运动目标检测方法,应用场景中的光照变化会极大影响现存变分光流法的稳定性及准确率,提出基于分数阶的变分光流模型来提高光照变化鲁棒性.该模型将分数阶导数同时应用于经典变分光流模型的数据项及平滑项中;根据图像的数据特征,采用图像函数及光流向量函数的有限离散二重分数阶导数近似拟合求导结果计算光流向量,进而将光...     

一类广义变分不等式问题的神经网络模型

基于解的充分必要条件,提出一类广义变分不等式问题的神经网络模型.通过构造Lyapunov函数,在适当的条件下证明了新模型是Lyapunov稳定的,并且全局收敛和指数收敛于原问题的解.数值试验表明,该神经网络模型是有效的和可行的.     

A Multi‐Model Approach for the Efficient Solution of Differential‐Algebraic Boundary Value Problems

A multi‐model approach is presented which allows the efficient and stable coupling between high precision algorithms for DAE boundary value problems arising from constrained optimal control problems and model data obtained with rather low accuracy from finite element solutions of PDEs. A model hierarchy with increasing approximation accuracy serves as an intermediate layer. Numerical efficiency is demonstrated for an example from flight mechanics.     

Convergence of Hybrid Steepest-Descent Methods for Generalized Variational Inequalities

In this paper, we consider the generalized variational inequality GVI（F, g, C）, where F and g are mappings from a Hilbert space into itself and C is the fixed point set of a nonexpansive mapping. We propose two iterative algorithms to find approximate solutions of the GVI（F,g, C）. Strong convergence results are established and applications to constrained generalized pseudo-inverse are included.     

A General Algorithm and Sensitivity Analysis for Variational Inequalities

The fixed point technique is used to prove the existence of a solution for a class of variational inequalities related with odd order boundary value problems and to suggest a general algorithm. We also make the sensitivity analysis for these variational inequalities and complementarity problems using the projection technique. Several special cases are discussed, which can be obtained from our results.     

A Discussion on Variational Analysis in Derivative-Free Optimization

Variational Analysis studies mathematical objects under small variations. With regards to optimization, these objects are typified by representations of first-order or second-order information (gradients, subgradients, Hessians, etc). On the other hand, Derivative-Free Optimization studies algorithms for continuous optimization that do not use first-order information. As such, researchers might conclude that Variational Analysis plays a limited role in Derivative-Free Optimization research. In this paper we argue the contrary by showing that many successful DFO algorithms rely heavily on tools and results from Variational Analysis.