Quasi-variational principle for the vortex-potential function of rotational flow in three-dimension pipe

The variational analysis of the Pseudo-potential function-vortex-potential function model, a new mathematical model, was developed and by which the flow field with transonic speed and curl was decided, and different sorts of the variational principle for vortex potential function were established by transforming the original equation for vortex-function,the boundary conditions for vortex-potential function was raised.     

Large-deflection bending of symmetrically laminated rectilinearly orthotropic elliptical plates including transverse shear

Summary The nonlinear bending theory for symmetrically laminated elliptical plates exhibiting rectilinear orthotropy with transverse shear deformation is developed. Using Galerkin's method, the paper solves the problem of large deflections for plates under uniform lateral pressure. The special case of symmetrically laminated rectilinearly orthotropic circular plates is also discussed. Analytical solutions obtained may be applied directly to the design of engineering structures. Received 6 March 1995; accepted for publication 8 January 1997     

Thermal bending of thick rectangular plates of bimodulus composite materials

Wiighted residual solutions are presented for thermal bending of laminated composite plates. The material of each layer is assumed to be clastically and thermoelastically orthotropic and bimodular. The formulations are based on the thermoclastic version of the theory of Whitney-Pagano laminated plate, which includes thickness shear detormations. The results are obtained for deflections and neutral-surface positions and are found to be in good agreement with the closed-form solution.     

Geometrically nonlinear isogeometric analysis of laminated composite plates based on higher-order shear deformation theory

In this paper, we present an effectively numerical approach based on isogeometric analysis (IGA) and higher-order shear deformation theory (HSDT) for geometrically nonlinear analysis of laminated composite plates. The HSDT allows us to approximate displacement field that ensures by itself the realistic shear strain energy part without shear correction factors (SCFs). IGA utilizing basis functions namely B-splines or non-uniform rational B-splines (NURBS) enables to satisfy easily the stringent continuity requirement of the HSDT model without any additional variables. The nonlinearity of the plates is formed in the total Lagrange approach based on the small strain assumptions. Numerous numerical validations for the isotropic, orthotropic, cross-ply and angle-ply laminated plates are provided to demonstrate the effectiveness of the proposed method.     

Nonlinear bending of simply supported symmetric laminated cross-ply rectangular plates

Based on the von Kármán-type theory of plates,nonlinear bending problems of simplysupported symmetric laminated cross-ply rectangular plates under the combined action ofpressure and inplane load are investigated in this paper.The solution which satisfies thegoverning equations and boundary conditions is obtained by using the double Fourier seriesmethod.     

Theory of nonlinear dynamic stability for composite laminated plates

In this paper,the general equations of dynamic stability for composite laminatedplates are derived by Hamilton principle.These general equations can be used to considerthose different factors that affect the dynamic stability of laminated plates.The factors aretransverse shear deformation,initial imperfections,longitudinal and rotational inertia,andply-angle of the fiber,etc.The solutions of the fundamental equations show that someimportant characteristics of the dynamic instability can only be got by the considerationand analysis of those factors     

ANALYSIS OF SYMMETRIC LAMINATED RECTANGULAR PLATES IN PLANE STRESS

Symmetric laminated plates used usually are anisotropic plates. Based on the fundamental equation for anisotropic rectangular plates in plane stress problem, a general analytical solution is established accurately by method of stress function. Therefore the general formula of stress and displacement in plane is given. The integral constants in general formula can be determined by boundary conditions. This general solution is composed of solutions made by trigonometric function and hyperbolic function, which can satisfy the problem of arbitrary boundary conditions along four edges, and the algebraic polynomial solutions which can satisfy the problem of boundary conditions at four corners. Consequently this general solution can be used to solve the plane stress problem with arbitrary boundary conditions. For example, a symmetric laminated square plate acted with uniform normal load, tangential load and nonuniform normal load on four edges is calculated and analyzed.     

Stochastic nonlinear bending response of laminated composite plates with system randomness under lateral pressure and thermal loading

In this paper, the effect of sensitivity of randomness in system parameters on the nonlinear transverse central deflection response of laminated composite plates subjected to transverse uniform lateral pressure and thermal loading is examined. System parameters such as the lamina material properties, expansion of thermal coefficients, lamina plate thickness and lateral load are modelled as basic random variables. A higher order shear deformation theory in the von-Karman sense is used to model the system behavior of the laminated plate. A direct iterative-based C ⁰ nonlinear finite element method in conjunction with the first-order perturbation technique developed by the authors is extended for thermal problem to obtain the second-order response statistics, i.e., mean and variance of the nonlinear transverse deflection of the plate. Typical numerical results of composite plates with temperature independent and dependent material properties subjected to uniform temperature and combination of uniform and transverse temperature are obtained for various combinations of geometric parameters, uniform lateral pressures, staking sequences and boundary conditions. The results have been compared with those available in the literature and an independent Monte Carlo simulation.     

A stabilized complementarity formulation for nonlinear analysis of 3D bimodular materials

Bi-modulus materials with different mechanical responses in tension and compression are often found in civil, composite, and biological engineering. Numerical analysis of bimodular materials is strongly nonlinear and convergence is usually a problem for traditional iterative schemes. This paper aims to develop a stabilized computational method for nonlinear analysis of 3D bimodular materials. Based on the parametric variational principle, a unified constitutive equa-tion of 3D bimodular materials is proposed, which allows the eight principal stress states to be indicated by three para-metric variables introduced in the principal stress directions. The original problem is transformed into a standard linear complementarity problem (LCP) by the parametric virtual work principle and a quadratic programming algorithm is developed by solving the LCP with the classic Lemke’s algo-rithm. Update of elasticity and stiffness matrices is avoided and, thus, the proposed algorithm shows an excellent conver-gence behavior compared with traditional iterative schemes. Numerical examples show that the proposed method is valid and can accurately analyze mechanical responses of 3D bimodular materials. Also, stability of the algorithm is greatly improved.     

An enhanced single-layer variational formulation for the effect of transverse shear on laminated orthotropic plates

A novel mixed formulation is derived by means of Reissner's variational approach-based on Castigliano's principle of least work in conjunction with a Lagrange multiplier method for the calculus of variations. The governing equations present an alternative theory for modeling the important three-dimensional structural aspects of plates in a two-dimensional form. By integrating the classical Cauchy's equilibrium equations with respect to the thickness co-ordinate, and enforcing continuity of shear and normal stresses at each ply interface, condenses the effect of the thickness. A reduced system of partial differential equations of sixth-order in one variable, is also proposed, which contains differential correction factors that formally modify the classical constitutive equations for composite laminates. The theory degenerates to classical composite plate analysis for thin configurations. Significant deviations from classical plate theory are observed when the thickness becomes comparable with the in-plane dimensions. A variety of case studies are presented and solutions are compared with other models available in the literature and with finite element analysis.     

Mechanical behaviour of laminated composite beam by the new multi-layered laminated composite structures model with transverse shear stress continuity

This work presents a new multi-layer laminated composite structure model to predict the mechanical behaviour of multi-layered laminated composite structures. As a case study, the mechanical behaviour of laminated composite beam (90°/0°/0°/90°) is examined from both a static and dynamic point of view. The results are compared with the model “Sinus” and finite element method studied by Abou Harb. Results show that this new model is more precise than older ones as compared to the results by the finite element method (Abaqus). To introduce continuity on the interfaces of each layer, the kinematics defined by Ossadzow was used. The equilibrium equations and natural boundary conditions are derived by the principle of virtual power. To validate the new proposed model, different cases in bending, buckling and free vibration have been considered.     

Complex potential formalisms for bending of inhomogeneous monoclinic plates including transverse shear deformation

This paper develops complex potential formalisms for the solution of the bending problem of inhomogenoeus anisotropic plates, on the basis of the most commonly used refined plate theories. Being an initial step in that direction, it works out such formalisms only in connection with the bending problem of shear deformable homogeneous plates as well as plates having a special type of inhomogeneity along their thickness direction. The adopted type of inhomogeneity is however still general enough to include certain classes of plates made of functionally graded material as well as the classes of cross- and angle-ply symmetric laminates as particular cases. The basic formalism, similar to that developed by Stroh in plane strain elasticity, is detailed in relation with the equilibrium equations of a generalized plate theory that accounts for the effects of transverse shear deformation and includes conventional, refined theories as particular cases. Some interesting specializations, related to the most important of those conventional plate theories, are then presented and discussed separately. Hence, the outlined formalisms provide, for the first time in analytical form, the general solution of the partial differential equations associated with the most commonly used refined, elastic plate theories.     

组合荷载作用下层合板非线性弯曲的半解析摄动DQ法

研究不同边界约束层合薄板在面内与横向组合荷载作用下的非线性弯曲问题，给出了基于摄动技术，单向DQ格式和Galerkin法的半解析法，算例表明该方法是可靠有效的。     

Theoretical and experimental studies on nonlinear oscillations of symmetric cross-ply composite laminated plates

The nonlinear oscillations and resonant responses of the symmetric cross-ply composite laminated plates are investigated theoretically and experimentally. The governing equations of motion for the composite laminated plate are derived by using the von Karman type equation, Reddy’s third-order shear deformation plate theory, and Galerkin method with the geometric nonlinearity. The four-dimensional averaged equation is obtained by using the method of multiple scales. The frequency-response functions are analyzed under the consideration of strongly coupled of two modes. The influences of the resonance case on the softening and hardening type of nonlinearity are analyzed with different parameters for the composite laminated plates. The numerical results indicate that there exist the hardening and softening types of the composite laminated plate in the specific resonant case. The variation of the response amplitudes is studied for the composite laminated plate under combined the transverse and in-plane excitations. A sweep frequency experiment is performed to obtain the hardening and softening nonlinearities of a composite laminated plate. The experimental results coincide with the numerical results qualitatively. The influences of the excitation amplitudes on the softening and hardening types of nonlinearity are also analyzed for the composite laminated plate. The amplitude spectrums of the test plate also demonstrate that the change of the nonlinear dynamic responses may be caused by the subharmonic resonance.     

Bending of cantilever rectangular plates with the effect of transeverse shear deformation

On the basis of Reissner's theory, the exact solutions of the bending of cantilever rectangular plates are obtained by means of the concept of generalized simply-supported boundary. From the results obtained, it can be found that the method is valid.     

集中载荷作用下不同边界条件的弯曲厚矩形板的受迫振动

运用边界积分法研究了四边简支、两对边固定另两对边简支、四边固定三种复杂边界条件下厚矩形板的受迫振动问题,求解过程清晰,从而给出了受迫振动控制方程和挠曲面方程。通过在Matlab平台上进行数值计算,得出了图表形式的计算结果,并与有限元模拟值进行对照。研究表明,边界积分法用于求解厚矩形板的受迫振动问题的准确性,本文推导的控制方程和挠曲面方程的正确性,进而对工程实际中的各种相关问题具有一定的现实意义,也为求解此类问题提供了一种新途径,可以直接运用到工程实际中。