用于AGS结构分析的混合法

结合均匀化模型和加筋单元模型构造了一种混合模型用来分析复合材料格栅加筋板/壳结构（AGS）。所构造的加筋单元模型是一种高性能协调转角独立加筋板壳单元,保持了肋骨和蒙皮位移场的协调性,同时还满足肋骨和蒙皮具有独立转动条件,该单元中肋骨的方向和位置任意。混合法具有精度高、速度快等特点。通过典型算例讨论了肋骨间距和高度对均匀化模型计算结果精度的影响,通过对带孔复合材料AGS板孔边特殊点应力值的分析证明了混合法的有效性。      

A fully automatic force method for the optimal shakedown design of frames

The paper presents a fully automatic way to handle the problem of the optimal shakedown design of planar frames. The evaluation of the elastic moments is essential for this design problem and due to the fact that they are design dependent, a classical iterative procedure is followed which updates these moments at the beginning of each iteration. A linear programming problem is then solved inside each iteration. The formulation adopted here is based on the force method which has computational advantages against the displacement method for this type of problems. Within the framework of the force method, the statical basis is provided by an easy to implement algorithm which selects a near minimal mesh basis for any planar graph. This basis is efficiently used, in a novel way, to find the flexibility matrix of the frame in a skyline form amenable to standard algorithms for its decomposition. The quickest way to the ground of each load is used to form the right hand side of the elastic compatibility equations for each load pattern. These equations are efficiently solved by standard back-substitution algorithms and the elastic bending moments to be introduced at the beginning of each iteration is established. Examples of application are also included.     

A hybrid stiffness matrix for orthotropic sandwich plates with thick faces

A stiffness matrix is derived for a rectangular orthotropic sandwich plate element with thick faces by the assumed stress hybrid approach. It will be demonstrated that an independent polynomial can be used for the internal forces of the sandwich plate by the membrane theory (assumption of thin faces) and also for the additional moments and shear forces of the faces. The boundary displacements are approached solutions of the homogeneous differential equation of a sandwich beam.     

Vibration of frames and other structures with banded stiffness matrix

A general digital computer method based on a Sturm sequence procedure is described for determining the natural frequencies and associated modes of undamped free vibration of frames and other structures whose stiffness and mass matrices are of band form. A program which uses the method for the analysis of plane multi-storey building frames is outlined, and numerical results are presented for a simple test case and for a 19-storey frame.     

Non-linear vibration of frames by the incremental dynamic stiffness method

The dynamic stiffness method is extended to large amplitude free and forced vibrations of frames. When the steady state vibration is concerned, the time variable is replaced by the frequency parameter in the Fourier series sense and the governing partial differential equations are replaced by a set of ordinary differential equations in the spatial variables alone. The frequency-dependent shape functons are generated approximately for the spatial discretization. These shape functions are the exact solutions of a beam element subjected to mono-frequency excitation and constant axial force to minimize the spatial discretization errors. The system of ordinary differential equations is replaced by a system of non-linear algebraic equations with the Fourier coefficients of the nodal displacements as unknowns. The Fourier nodal coefficients are solved by the Newtonian algorithm in an incremental manner. When an approximate solution is available, an improved solution is obtained by solving a system of linear equations with the Fourier nodal increments as unknowns. The method is very suitable for parametric studies. When the excitation frequency is taken as a parameter, the free vibration response of various resonances can be obtained without actually computing the linear natural modes. For regular points along the response curves, the accuracy of the gradient matrix (Jacobian or tangential stiffness matrix) is secondary (cf. the modified Newtonian method). However, at the critical positions such as the turning points at resonances and the branching points at bifurcations, the gradient matrix becomes important. The minimum number of harmonic terms required is governed by the conditions of completeness and balanceability for predicting physically realistic response curves. The evaluations of the newly introduced mixed geometric matrices and their derivatives are given explicitly for the computation of the gradient matrix.     

A consistent tangent stiffness matrix for three-dimensional non-linear contact analysis

A consistent tangent stiffness matrix for the analysis of non-linear contact problems is presented. The associated element has three or four nodes and establishes contact between three-dimensional structures like solids and shells. It accounts for the non-linear kinematics of large deformation analysis and guarantees a quadratic convergence rate. Two formulations, the penalty method and the Lagrange multiplier method, are investigated.     

A mathematical programming method for the inelastic analysis of reinforced concrete frames

A mathematical programming method is presented for solving problems of (i) determining the moments and rotations and (ii) determining the safety factor of reinforced concrete frames. The proposed method is essentially a reformulation of those developed by De Donato and Maier. However, the reformulation results in a new mathematical programming model for which an efficient algorithm is developed. The advantage of the proposed method is mainly computational; in fact it requires roughly one half computer time and storage space as compared with those De Donato and Maier employ to solve the same problem.     

A fast multipole hybrid boundary node method for composite materials

This article presents a multi-domain fast multipole hybrid boundary node method for composite materials in 3D elasticity. The hybrid boundary node method (hybrid BNM) is a meshless method which only requires nodes constructed on the surface of a domain. The method is applied to 3D simulation of composite materials by a multi-domain solver and accelerated by the fast multipole method (FMM) in this paper. The preconditioned GMRES is employed to solve the final system equation and precondition techniques are discussed. The matrix–vector multiplication in each iteration is divided into smaller scale ones at the sub-domain level and then accelerated by FMM within individual sub-domains. The computed matrix–vector products at the sub-domain level are then combined according to the continuity conditions on the interfaces. The algorithm is implemented on a computer code written in C + +. Numerical results show that the technique is accurate and efficient.     

A health management algorithm for composite train carbody based on FEM/FBG hybrid method

In this study, a health management program for a composite train carbody was developed using the acquired strain distributions from fiber Bragg grating (FBG) sensor arrays. To determine appropriate locations for the FBG sensors, a finite element analysis (FEA) was executed. In this FEA, a FE model of the Korean tilting train (TTX) was used as a representative composite carbody train. The FEA results of various derailment situations and high speed operation on curved track were used as the database of each deformation case. In the last step, the health management program was produced using LabVIEW software. In this post-processing algorithm, the method of least squares was used to determine the difference between the FEA results and the acquired strains. This program shows the estimated deformations and plots of the acquired strains, as well as displaying an emergency indicator when necessary, all through post-processing of the strains. Finally, this FEM/FBG hybrid method was verified by several simulations using the reproductive sensor data.     

双闭室复合材料薄壁梁的结构阻尼细观分析

研究双闭室复合材料薄壁梁的结构阻尼特性。基于单层混杂材料的细观力学阻尼计算方法和多胞模型,分别获得单层复合材料的等效阻尼特性和等效弹性特性;基于变分渐进法（VAM)和Hamilton原理,建立双闭室复合材料薄壁梁振动方程;采用Galerkin法对薄壁梁进行自由振动分析;在获得薄壁梁振动模态矢量的基础上,根据最大应变能理论,对薄壁梁的模态阻尼性能进行预测,并且将阻尼预测的结果与现有的有限元计算结果进行对比,验证了本文阻尼分析模型的有效性。进一步针对四种种构型双闭室复合材料薄壁箱形梁,进行阻尼计算,揭示了纤维铺层角和纤维含量的影响。     

A computationally efficient method for the limit elasto plastic analysis of space frames

A computationally efficient method for the first order step-by-step limit analysis of space frames is presented. The incremental non-holonomic analysis is based on the generalized plastic node method. The non-linear yield surface is approximated by a multi-faceted surface, thus avoiding the iterative formulation at each load step. In order to prevent the occurrence of very small load steps a second internal and homothetic to the initial yield surface is implemented which creates a plastic zone for the activation of the plastic modes. This implementation reduces substantially the computational effort of the procedure without affecting the value of the final load. The solution of the linear equilibrium equation at each load step is obtained with the preconditioned conjugate gradient method. Special attention is paid to the fact that the overall stiffness matrix changes gradually with the successive formation of plastic nodes. The application of the conjugate gradient method is based on some recent developments on improved matrix handling techniques and efficient preconditioning strategies. A number of test problems have been performed which show the usefulness of the proposed approach and its superiority in respect to efficient direct methods of solution in both storage requirements and computing time.     

Elastic buckling analysis of 3-D trusses and frames with thin-walled members

 A finite element method is presented for the determination of the elastic buckling load of three-dimensional trusses and frames with rigid joints. The beam element stiffness matrix is constructed on the basis of the exact solution of the governing equations describing the coupled flexural-torsional buckling behaviour of a three-dimensional beam with an open thin-walled section in the framework of a small deformation theory. Large deformation effects are taken into account approximately through consideration of P−Δ effects. The structural stiffness matrix is obtained by an appropriate superposition of the various element stiffness matrices. The axial force distribution in the members is obtained iteratively for every value of the externally applied loading and the vanishing of the determinant of the structural stiffness matrix is the criterion used to numerically determine the elastic buckling load of the structure. The effect of initial member imperfections is also included in the formulation. Comparisons of accuracy and efficiency of the present exact finite element method against the conventional approximate finite element method are made. Cases where the axial force distribution determination can be done without iterations are also identified. The effect of neglecting the warping stiffness of some mono-symmetric sections is also investigated. Numerical examples involving simple and complex three-dimensional trusses and frames are presented to illustrate the method and demonstrate its merits. Received: 2 May 2000 / Accepted: 15 July 2002     

Exact stiffness matrix of mono-symmetric composite I-beams with arbitrary lamination

The exact stiffness matrix, based on the simultaneous solution of the ordinary differential equations, for the static analysis of mono-symmetric arbitrarily laminated composite I-beams is presented herein. For this, a general thin-walled composite beam theory with arbitrary lamination including torsional warping is developed by introducing Vlasov’s assumption. The equilibrium equations and force–deformation relations are derived from energy principles. The explicit expressions for displacement parameters are then derived using the displacement state vector consisting of 14 displacement parameters, and the exact stiffness matrix is determined using the force–deformation relations. In addition, the analytical solutions for symmetrically laminated composite beams with various boundary conditions are derived as a special case. Finally, a finite element procedure based on Hermitian interpolation polynomial is developed. To demonstrate the validity and the accuracy of this study, the numerical solutions are presented and compared with the analytical solutions and the finite element results using the Hermitian beam elements and ABAQUS’s shell element.     

A new hybrid method for fault tree analysis

This paper describes a new method for determining the significant minimal cut sets of complex fault trees. It can be classified as hybrid, being based on the application of both Top Down and Bottom Up reduction approaches. This solution has been adopted particularly to accurately estimate the truncation error when the probabilistic cut-off technique is applied. Experimental results on real fault trees proved that the degree of conservatism of the truncation error is negligible at any practical combination of the probabilistic and logical threshold values.This new fault tree analysis procedure has been implemented, in C language, in the second version of the computer programme ISPRA-FTA.     

Vibration analysis of thin-walled composite beams with I-shaped cross-sections

A general analytical model applicable to the vibration analysis of thin-walled composite I-beams with arbitrary lay-ups is developed. Based on the classical lamination theory, this model has been applied to the investigation of load–frequency interaction curves of thin-walled composite beams under various loads. The governing differential equations are derived from the Hamilton’s principle. A finite element model with seven degrees of freedoms per node is developed to solve the problem. Numerical results are obtained for thin-walled composite I-beams under uniformly distributed load, combined axial force and bending loads. The effects of fiber orientation, location of applied load, and types of loads on the natural frequencies and load–frequency interaction curves as well as vibration mode shapes are parametrically studied.     

Coupled deflection analysis of thin-walled Timoshenko laminated composite beams

For the deflection analyses of thin-walled Timoshenko laminated composite beams with the mono- symmetric I-, channel-, and L-shaped sections, the stiffness matrices are derived based on the solutions of the simultaneous ordinary differential equations. A general thin-walled composite beam theory considering shear deformation effect is developed by introducing Vlasov’s assumptions. The shear stiffnesses of thin-walled composite beams are explicitly derived from the energy equivalence. The equilibrium equations and force-deformation relations are derived from energy principles. By introducing 14 displacement parameters, a generalized eigenvalue problem that has complex eigenvalues and multiple zero eigenvalues is formulated. Polynomial expressions are assumed as trial solutions for displacement parameters and eigenmodes containing undetermined parameters equal to the number of zero eigenvalues are determined by invoking the identity condition to the equilibrium equations. Then the displacement functions are constructed by combining eigenvectors and polynomial solutions corresponding to nonzero and zero eigenvalues, respectively. Finally, the stiffness matrices are evaluated by applying the member force-displacement relations to the displacement functions. In addition, the finite beam element formulation based on the classical Lagrangian interpolation polynomial is presented. In order to verify the validity and the accuracy of this study, the numerical solutions are presented and compared with the finite element results using the isoparametric beam elements and the detailed three-dimensional analysis results using the shell elements of ABAQUS. Particularly the effects of shear deformations on the deflection of thin-walled composite beams with the mono-symmetric I-, channel-, and L-shaped sections with various lamination schemes are investigated.     

A simple and efficient solution method for the limit elasto-plastic analysis of plane frames

A solution method for the first order step-by-step limit analysis of plane frames is presented. The formulation of the governing equations is based on the plastic node method and takes into account stress reversals and any type of yield conditions. The solution of the governing equilibrium equations in each step is obtained with the preconditioned conjugate gradient method. Special attention is paid to the fact that the overall stiffness matrix changes gradually with the successive formation of plastic nodes. A number of test problems have been performed which show the usefulness of the present approach. The results also reveal the superiority of this technique, in both storage requirements and computing time, with respect to efficient methods of solution.     

Improvement of the bonding interface in hybrid fiber/particle preform reinforced Al matrix composite

The bonding interface between the reinforcement and the matrix alloy in hybrid AZS fiber/SiC particle preform based aluminum metal matrix composites (Al MMCs) has been investigated as a function of reinforced particle size and the binder content. It is observed that high binder and large particle will result in a poor bonding interface. This has deleterious effects on the mechanical properties of the cast MMCs. Estimation of the binder thickness indicates that there exists a critical particle size above which the particles are not appropriate to be used in fabricating the hybrid fiber/particle preform based MMCs.