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.

A Molecular Dynamics Simulation for Periodic Boundary Condition in the Bending Process of Ag／Ni Composite Interfaces

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NUMERICAL SIMULATION OF 2D FIBER-REINFORCED COMPOSITES USING BOUNDARY ELEMENT METHOD

The boundary dement method was improved for the 2D elastic composites with randomly distributed inclusions. This problem can be reduced to a boundary integral equation for a multi-connected domain. Further, considering the matrices of the tractions and displacements for each group of the identical inclusion were the same, an effective computational scheme was designed, since the orders of the resulting matrix equations can be greatly reduced. Numerical examples indicate that this boundary element method scheme is more effective than the conventional multi-domain boundary element method for such a problem. The present scheme can be used to investigate the effective mechanical properties of the fiber-reinforced composites.

STOCHASTIC BOUNDARY ELEMENT METHOD FOR RELIABILITY ANALYSIS OF PLATE AND BEAMS COMPOSITE STRUCTURES

In this paper, the reliability of orthotropic plate and beams composite structures, which is under the actions of the stochastic loading and stochastic boundary conditions, have been analyzed by stochastic boundary element method. First, the boundary integral equation of orthotropic plate and beams composite structures is given in this paper, and then based on the stochastic boundary element method, the method for reliability analysis of stochastic structures is establishes and formulas for computation of reliability index of orthotropic plate and beams composite structures are obtained. The computed examples show the efficient of the method used in this paper.

Effects of Boundary Conditions on Postbuckling Strengths of Composite Laminate with Various Shaped Cutouts under In-Plane Shear

Cutouts are often provided in composite structural components for practical reasons. For instance, aircraft components such as wingspar, fuselage and ribs are provided with cutouts for access, inspection, fuel lines and electric lines or to reduce the overall weight. This paper addresses the effect of boundary condition on buckling and postbuckling responses, failure loads, and failure characteristics of composite laminate with various shaped cutouts (i.e., circular, square, diamond, elliptical-vertical and elliptical-horizontal) and having different lay-ups under in-plane shear (positive and negative) load, using finite-element method. The FEM formulation is based on the first order shear deformation theory in conjunction with geometric nonlinearity using von Karman’s assumptions. The 3-D Tsai-Hill criterion is used to predict the failure of a lamina while the onset of delamination is predicted by the interlaminar failure criterion. It is observed that the effect of boundary condition on buckling, first-ply failure and ultimate failure loads of a quasi-isotropic laminate with cutout is more for positive shear load than that for the negative shear load for almost all cutout shapes. It is also noted that under in-plane shear loads postbuckling stiffness of (0/90)4s laminate with circular cutout is maximum, while it is minimum for (45/—45)4s laminate with circular cutout, irrespective of boundary conditions.

The Calculation of Stress-Strain State of Anisotropic Composite Finite-Element Area with Different Boundary Conditions on the Surface

The numerical analytic research approach of stress-strain state of anisotropic composite finite element area with different boundary conditions on the surface, is represented below. The problem is solved by using a spatial model of the elasticity theory. Differential equation system in partial derivatives reduces to one-dimensional problem using spline collocation method in two coordinate directions. Boundary problem for the system of ordinary higher-order differential equation is solved by using the stable numerical technique of discrete orthogonalization.

BOUNDARY ELEMENT METHOD FOR MODEL ANALYSIS OF 2-D COMPOSITE STRUCTURE

The boundary element method is used for he modal analysis of freevibration of 2-D composite structures in this paper. Since theparticular solution method is used to treat the terms of body forces(inertial forces) in the equation of motion, only static fundamentalsolutions are needed in solving the problem. For an isotropiccantilever beam, the numerical results obtained by using the BEMpresented in this paper are in good agreement, with those of usingFEM or other BEM, but this BEM can also be used to analyze problemsfor anisotropic materials.

A parallel fast multipole BEM and its applications to large-scale analysis of 3-D fiber-reinforced composites

In this paper, an adaptive boundary element method （BEM） is presented for solving 3-D elasticity problems. The numerical scheme is accelerated by the new version of fast multipole method （FMM） and parallelized on distributed memory architectures. The resulting solver is applied to the study of representative volume element （RVE） for short fiberreinforced composites with complex inclusion geometry. Numerical examples performed on a 32-processor cluster show that the proposed method is both accurate and efficient, and can solve problems of large size that are challenging to existing state-of-the-art domain methods.

Fabrication and performance of La(0.8)Sr(0.2)MnO3/YSZ graded composite cathodes for SOFC

The performance of multi-layer （1 -x）La0.8Sr0.2MnO3/xYSZ graded composite cathodes was studied as electrode materials for intermediate solid oxide fuel cells （SOFC）. The thermal expansion coefficient, electrical conductivity, and electrochemical performance of multi-layer composite cathodes were investigated. The thermal expansion coefficient and electrical conductivity decreased with the increase in YSZ content. The （1 -x）Lao.sSr0.EMnO3/xYSZ composite cathode greatly increased the length of the active triple phase boundary line （TPBL） among electrode, electrolyte, and gas phase, leading to a decrease in polarization resistance and an increase in polarization current density. The polarization current density of the triple-layer graded composite cathode （0.77 A/cm2） was the highest and that of the monolayer cathode （0.13 A/cm2） was the lowest. The polarization resistance （Rp） of the triple-layer graded composite cathode was only 0.182 Ω·cm2 and that of the monolayer composite cathode was 0.323 Ω·cm2. The power density of the triple-layer graded composite cathode was the highest and that of the monolayer composite cathode was the lowest. The triple-layer graded composite cathode had superior performance.

SOLUTION OF DIFFERENT HOLES SHAPE BORDERS OF FIBRE REINFORCED COMPOSITE PLATES BY INTEGRAL EQUATIONS

Accurate boundary conditions of composite material plates with different holes are founded to settle boundary condition problems of complex holes by conformal mapping method upon the nonhomogeneous anisotropic elastic and complex function theory. And then the two stress functions required were founded on Cauchy integral by boundary conditions. The final stress distributions of opening structure and the analytical solution on composite material plate with rectangle hole and wing manholes were achieved. The influences on hole-edge stress concentration factors are discussed under different loads and fiber direction cases, and then contrast calculates are carried through FEM.

An efficient SPH methodology for modelling mechanical characteristics of particulate composites

Particulate composites are one of the widely used materials in producing numerous state-of-the-art components in biomedical,automobile,aerospace including defence technology.Variety of modelling techniques have been adopted in the past to model mechanical behaviour of particulate composites.Due to their favourable properties,particle-based methods provide a convenient platform to model failure or fracture of these composites.Smooth particle hydrodynamics(SPH)is one of such methods which demonstrate excellent potential for modelling failure or fracture of particulate composites in a Lagrangian setting.One of the major challenges in using SPH method for modelling composite materials depends on accurate and efficient way to treat interface and boundary conditions.In this paper,a masterslave method based multi-freedom constraints is proposed to impose essential boundary conditions and interfacial displacement constraints in modelling mechanical behaviour of composite materials using SPH method.The proposed methodology enforces the above constraints more accurately and requires only smaller condition number for system stiffness matrix than the procedures based on typical penalty function approach.A minimum cut-off value-based error criteria is employed to improve the computational efficiency of the proposed methodology.In addition,the proposed method is further enhanced by adopting a modified numerical interpolation scheme along the boundary to increase the accuracy and computational efficiency.The numerical examples demonstrate that the proposed master-slave approach yields better accuracy in enforcing displacement constraints and requires approximately the same computational time as that of penalty method.

Efficient 2D Analysis of Interfacial Thermoelastic Stresses in Multiply Bonded Anisotropic Composites with Thin Adhesives

In engineering practice,analysis of interfacial thermal stresses in composites is a crucial task for assuring structural integrity when sever environmental temperature changes under operations.In this article,the directly transformed boundary integrals presented previously for treating generally anisotropic thermoelasticity in two-dimension are fully regularized by a semi-analytical approach for modeling thin multi-layers of anisotropic/isotropic composites,subjected to general thermal loads with boundary conditions prescribed.In this process,an additional difficulty,not reported in the literature,arises due to rapid fluctuation of an integrand in the directly transformed boundary integral equation.In conventional analysis,thin adhesives are usually neglected due to modeling difficulties.A major concern arises regarding the modeling error caused by such negligence of the thin adhesives.For investigating the effect of the thin adhesives considered,the regularized integral equation is applied for analyzing interfacial stresses in multiply bonded composites when thin adhesives are considered.Since all integrals are completely regularized,very accurate integration values can be still obtained no matter how the source point is close to the integration element.Comparisons are made for some examples when the thin adhesives are considered or neglected.Truly,this regularization task has laid sound fundamentals for the boundary element method to efficiently analyze the interfacial thermal stresses in 2D thin multiply bonded anisotropic composites.

An R(x)-orthonormal theory for the vibration performance of a non-smooth symmetric composite beam with complex interface

A composite beam is symmetric if both the material property and support are symmetric with respect to the middle point. In order to study the free vibration performance of the symmetric composite beams with different complex nonsmooth/discontinuous interfaces, we develop an R(x)-orthonormal theory, where R(x) is an integrable flexural rigidity function. The R(x)-orthonormal bases in the linear space of boundary functions are constructed, of which the second-order derivatives of the boundary functions are asked to be orthonormal with respect to the weight function R(x). When the vibration modes of the symmetric composite beam are expressed in terms of the R(x)-orthonormal bases we can derive an eigenvalue problem endowed with a special structure of the coefficient matrix A :=[aij ],aij= 0 if i + j is odd. Based on the special structure we can prove two new theorems, which indicate that the characteristic equation of A can be decomposed into the product of the characteristic equations of two sub-matrices with dimensions half lower. Hence, we can sequentially solve the natural frequencies in closed-form owing to the specialty of A. We use this powerful new theory to analyze the free vibration performance and the vibration modes of symmetric composite beams with three different interfaces.

Effect of carbide formers on microstructure and thermal conductivity of diamond-Cu composites for heat sink materials

Diamond-copper composites were prepared by powder metallurgy,in which the diamond particles were pre-coated by magnetic sputtering with copper alloy containing a small amount of carbide forming elements(including B,Cr,Ti,and Si).The influence of the carbide forming element additives on the microstructure and thermal conductivity of diamond composites was investigated.It is found that the composites fabricated with Cu-0.5B coated diamond particles has a relatively higher density and its thermal conductivity approaches 300 W/(m·K).Addition of 0.5%B improves the interfacial bonding and decreases thermal boundary resistance between diamond and Cu,while addition of 1%Cr makes the interfacial layer break away from diamond surface.The actual interfacial thermal conductivity of the composites with Cu-0.5B alloy coated on diamond is much higher than that of the Cu-1Cr layer,which suggests that the intrinsic thermal conductivity of the interfacial layer is an important factor for improving the thermal conductivity of the diamond composites.

Computer simulated experiments on fracture toughness of particle-dispersed composites

The fracture behavior of a series of geometrically similar three point bend specimens is simulated by a nonlinear multi zone boundary element computer program. The material is based on Al 2O 3 SiC (p) ceramic in which particles are randomly dispersed in a relatively soft matrix. A single edge main crack and a large number of interfacial microcracks randomly distributed between particles and matrix are prescribed. The load deflection curve and the spread of the fracture process zone (FPZ) are observed with confidence. The computer simulated results show that the fracture toughness of the material increases with increasing specimen dimension and becomes constant when the specimen size exceeds a critical value. A practical specimen size for predicting the true fracture toughness of aggregate materials is proposed.

Vibration characteristics and flutter analysis of a composite laminated plate with a store

The effects of an external store on the flutter characteristics of a composite laminated plate in a supersonic flow are investigated. The Dirac function is used to formulate the interaction between the plate and the store. The first-order piston theory is used to describe the aerodynamic load. The governing equation of the composite laminated plate with an external store is established based on the Hamilton principle. The mode shapes are constructed by the admissible functions which axe a set of characteristic orthogonal polynomials generated directly by the Gram-Schmidt process, and the boundary constraint is modeled as the artificial springs. The frequency and mode shapes of the plate under different boundaries are determined by the Rayleigh-Ritz method. The validity of the proposed approach is confirmed by comparing the results with those obtained from the finite element method （FEM）. The effects of the mounting position, the center of gravity position and the mounting points spacing of the external store on the flutter boundary are discussed for both the simply supported and cantilever plates, respectively, which correspond to the two installation sites of the external store, i.e., the belly and wings of the aircraft.

Fracture analysis for torsion problems of a composite cylinder with curvilinear cracks

The Salnt-Venant torsion problems of a composite cylinder with curvilinear cracks were investigated. By considering the bimaterial interface as a boundary of the outer bar or inner one, the problem was reduced to the solution of boundary integral equations on the crack, external boundary and interface. Using the new boundary element method, some typical torsion problems of a composite cylinder involving a straight or kinked crack were calculated. The obtained results were compared with data in the literature to show validity and applicability of the present method.

Sectional Warping Corrective Model for Free Edge Stresses in Composite Laminates

The edge stress problem in composite laminates under uniform axial extension is analyzed. The displacement distribution in three directions along the thickness are derived respectively by use of the sectional warping corrective theory, and the hierarchical displacement functions are adopted in the width direction. Finally, based on the principle of virtual work, a special finite element model for boundary layer effects is obtained. Accuracy and convergence of the solution are studied, and the present resu...

Distortional buckling analysis of steel-concrete composite box beams considering effect of stud rotational restraint under hogging moment

Restrained distortional buckling is an important buckling mode of steel-concrete composite box beams(SCCBB)under the hogging moment.Rotational and lateral deformation restraints of the bottom plate by the webs are essential factors affecting SCCBB distortional buckling.Based on the stationary potential energy principle,the analytical expressions for the rotational restraint stiffness(RRS)of the web upper edge as well as the RRS and the lateral restraint stiffness(LRS)of the bottom plate were derived.Also,the SCCBB critical moment formula under the hogging moment was derived.Using twenty specimens,the theoretical calculation method is compared with the finite-element method.Results indicate that the theoretical calculation method can effectively and accurately reflect the restraint effect of the studs,top steel flange,and other factors on the bottom plate.Both the RRS and the LRS have a nonlinear coupling relationship with the external loads and the RRS of the web’s upper edge.Under the hogging moment,the RRS of the web upper edge has a certain influence on the SCCBB distortional buckling critical moment.With increasing RRS of the web upper edge,the SCCBB critical moment increases at first and then tends to be stable.

Convergence Properties of Local Defect Correction Algorithm for the Boundary Element Method

Sometimes boundary value problems have isolated regions where the solution changes rapidly.Therefore,when solving numerically,one needs a fine grid to capture the high activity.The fine grid can be implemented as a composite coarse-fine grid or as a global fine grid.One cheaper way of obtaining the composite grid solution is the use of the local defect correction technique.The technique is an algorithm that combines a global coarse grid solution and a local fine grid solution in an iterative way to estimate the solution on the corresponding composite grid.The algorithm is relatively new and its convergence properties have not been studied for the boundary element method.In this paper the objective is to determine convergence properties of the algorithm for the boundary element method.First,we formulate the algorithm as a fixed point iterative scheme,which has also not been done before for the boundary element method,and then study the properties of the iteration matrix.Results show that we can always expect convergence.Therefore,the algorithm opens up a real alternative for application in the boundary element method for problems with localised regions of high activity.