Least Square Finite Element Model for Analysis of Multilayered Composite Plates under Arbitrary Boundary Conditions

Laminated composites are widely used in many engineering industries such as aircraft, spacecraft, boat hulls, racing car bodies, and storage tanks. We analyze the 3D deformations of a multilayered, linear elastic, anisotropic rectangular plate subjected to arbitrary boundary conditions on one edge and simply supported on other edge. The rectangular laminate consists of anisotropic and homogeneous laminae of arbitrary thicknesses. This study presents the elastic analysis of laminated composite plates subjected to sinusoidal mechanical loading under arbitrary boundary conditions. Least square finite element solutions for displacements and stresses are investigated using a mathematical model, called a state-space model, which allows us to simultaneously solve for these field variables in the composite structure’s domain and ensure that continuity conditions are satisfied at layer interfaces. The governing equations are derived from this model using a numerical technique called the least-squares finite element method (LSFEM). These LSFEMs seek to minimize the squares of the governing equations and the associated side conditions residuals over the computational domain. The model is comprised of layerwise variables such as displacements, out-of-plane stresses, and in- plane strains, treated as independent variables. Numerical results are presented to demonstrate the response of the laminated composite plates under various arbitrary boundary conditions using LSFEM and compared with the 3D elasticity solution available in the literature.

L^P SOLUTION OF GENERAL MEAN-FIELD BSDES WITH CONTINUOUS COEFFICIENTS

In this paper we consider one dimensional mean-field backward stochastic differential equations(BSDEs)under weak assumptions on the coefficient.Unlike[3],the generator of our mean-field BSDEs depends not only on the solution(Y,Z)but also on the law PY of Y.The first part of the paper is devoted to the existence and uniqueness of solutions in Lp,1<p≤2,where the monotonicity conditions are satisfied.Next,we show that if the generator/is uniformly continuous in(μ,y,z),uniformly with respect to(t,ω) and if the terminal valueξbelongs to Lp(Ω,F,P)with 1<p≤2,the mean-field BSDE has a unique Lp solution.

CONTINUAL CONDITIONS BETWEEN LAYERS FOR LAMINATED PLATES

In this paper, various forms of functional on blending energy principles of composite laminated plates are gir en, which guarantee satisfied continual conditions of displacements and stress between layers, and then the reliability of the functional are proved by the computing example.

A, ■-Ω METHOD FOR 3-D EDDY CURRENT ANALYSIS

After the field equations and the snonumuoo conditions between the interfaces for 3D eddy current problems Under various gauges were discussed, it was pointed cut in this paper that using the magnetic vector potential A. the electric scalar potential and Coulomb gauge △ .A = 0 in eddy current regions and using the magntetic scalar potential Ω in the non-conducting regions are more suitable. All field equations, the boundary conditions, the interface continuity conditions and the corresponding variational principle of this method are also given

Half-global discretization algorithm based on rough set theory

It is being widely studied how to extract knowledge from a decision table based on rough set theory. The novel problem is how to discretize a decision table having continuous attribute. In order to obtain more reasonable discretization results, a discretization algorithm is proposed, which arranges half-global discretization based on the correlational coefficient of each continuous attribute while considering the uniqueness of rough set theory. When choosing heuristic information, stability is combined with rough entropy. In terms of stability, the possibility of classifying objects belonging to certain sub-interval of a given attribute into neighbor sub-intervals is minimized. By doing this, rational discrete intervals can be determined. Rough entropy is employed to decide the optimal cut-points while guaranteeing the consistency of the decision table after discretization. Thought of this algorithm is elaborated through Iris data and then some experiments by comparing outcomes of four discritized datasets are also given, which are calculated by the proposed algorithm and four other typical algorithras for discritization respectively. After that, classification rules are deduced and summarized through rough set based classifiers. Results show that the proposed discretization algorithm is able to generate optimal classification accuracy while minimizing the number of discrete intervals. It displays superiority especially when dealing with a decision table having a large attribute number.

COMPARISON THEOREMS FOR MULTI-DIMENSIONAL GENERAL MEAN-FIELD BDSDES

In this paper we study multi-dimensional mean-field backward doubly stochastic differential equations(BDSDEs),that is,BDSDEs whose coefficients depend not only on the solution processes but also on their law.The first part of the paper is devoted to the comparison theorem for multi-dimensional mean-field BDSDEs with Lipschitz conditions.With the help of the comparison result for the Lipschitz case we prove the existence of a solution for multi-dimensional mean-field BDSDEs with an only continuous drift coefficient of linear growth,and we also extend the comparison theorem to such BDSDEs with a continuous coefficient.

Numerical Simulation of Elastic Stress Wave Refraction at Air-Solid Interfaces

Elastic wave refraction at the air-solid interface and wave propagations in the vicinity of the air-solid interface are numerically studied.The modified ghost fluid method(MGFM)and isobaric fix methods are combined to solve the fluid and solid statuses at the air-solid interface and construct a continuous boundary condition for the air-solid interface.The states in the ghost domain are evaluated by the MGFM-algorithm.The solid governing equations are solved with second order spatial discretization.Numerical tests verify the correctness of the presented continuous boundary condition and show that the combined method is convergent in the vicinity of the air-solid interface.The 3D numerical results by the combined method are close to those of the ArbitraryLagrangian-Eulerian(ALE)method.The combined method is robust when applied for multi-dimensional problems.A compression stress wave impacting on the air-solid interface result in a compression wave in air.A tension stress wave impacting on the air-solid interface result in an expansion wave in air.

Generalized Backward Doubly Stochastic Differential Equations Driven by Lévy Processes with Continuous Coefficients

A new class of generalized backward doubly stochastic differential equations （GBDSDEs in short） driven by Teugels martingales associated with Levy process are investigated. We establish a comparison theorem which allows us to derive an existence result of solutions under continuous and linear growth conditions.

Benzene removal by nano magnetic particles under continuous condition from aqueous solutions

Benzene removal evaluated using Fe304 nano continuous condition. A 44 initial benzene concentration, from aqueous solutions was magnetic particles （NM） in factorial design including NM dose, contact time and pH was investigated in 16 experiments （Taguchi OA design）. The results indicated that all factors were significant and the optimum condition was： pH 8, NM dose of 2000 mg.L-1, benzene concentrations of 100 mg.L-1 and contact time of 14min. The maximum benzene uptake and distribution ratio in the optimum situation were 49.4mg.g-1 and 38.4L.g-1, respectively. The nano particles were shown to capture 98.7% of the benzene in optimum batch condition and 94.5% in continuous condition. The isotherm data proved that the Bmnauer-Emmett-Teller model fit more closely and produced an isotherm constant （b） less than one, indicating favorable adsorption. Regeneration studies verified that the benzene adsorbed by the NM could be easily desorbed by temperature, and thereby, NM can be employed repeatedly in water and wastewater management.

L^p SOLUTIONS TO BSDES WITH MONOTONIC AND UNIFORMLY CONTINUOUS GENERATORS

In this paper, we deal with Lp(p 】 1) solutions to one dimensional backward stochastic differential equations(BSDEs) with discontinuous(left or right continuous)generators. We obtain an existence theorem of Lpsolutions to BSDEs whose generators are discontinuous, monotonic in y and uniformly continuous in z.

Existence, Uniqueness and Approximation for Lp Solutions of Reflected BSDEs with Generators of One-sided Osgood Type

We prove several existence and uniqueness results for Lp （p 〉 1） solutions of reflected BSDEs with continuous barriers and generators satisfying a one-sided Osgood condition together with a general growth condition in y and a uniform continuity condition or a linear growth condition in z. A necessary and sufficient condition with respect to the growth of barrier is also explored to ensure the existence of a solution. And, we show that the solutions may be approximated by the penalization method and by some sequences of solutions of reflected BSDEs. These results are obtained due to the development of those existing ideas and methods together with the application of new ideas and techniques, and they unify and improve some known works.

Theoretical aspects of selecting repeated unit cell model in micromechanical analysis using displacement-based finite element method

Repeated Unit Cell（RUC）is a useful tool in micromechanical analysis of composites using Displacement-based Finite Element（DFE）method,and merely applying Periodic Displacement Boundary Conditions（PDBCs）to RUC is almost a standard practice to conduct such analysis.Two basic questions arising from this practice are whether Periodic Traction Boundary Conditions（PTBCs,also known as traction continuity conditions）are guaranteed and whether the solution is independent of selection of RUCs.This paper presents the theoretical aspects to tackle these questions,which unify the strong form,weak form and DFE method of the micromechanical problem together.Specifically,the solution’s independence of selection of RUCs is dealt with on the strong form side,PTBCs are derived from the weak form as natural boundary conditions,and the validity of merely applying PDBCs in micromechanical Finite Element（FE）analysis is proved by referring to its intrinsic connection to the strong form and weak form.Key points in the theoretical aspects are demonstrated by illustrative examples,and the merits of setting micromechanical FE analysis under the background of a clear theoretical framework are highlighted in the efficient selection of RUCs for Uni Directional（UD）fiber-reinforced composites.