Determination of stress intensity factors by the finite element discretized symplectic method

When rewriting the governing equations in Hamiltonian form, analytical solutions in the form of symplectic series can be obtained by the method of separation of variable satisfying the crack face conditions. In theory, there exists sufficient number of coefficients of the symplectic series to satisfy any outer boundary conditions. In practice, the matrix relating the coefficients to the outer boundary conditions is ill-conditioned unless the boundary is very simple, e.g., circular. In this paper, a new two-level finite element method using the symplectic series as global functions while using the conventional finite element shape functions as local functions is developed. With the available classical finite elements and symplectic series, the main unknowns are no longer the nodal displacements but are the coefficients of the symplectic series. Since the first few coefficients are the stress intensity factors, post-processing is not required. A number of numerical examples as well as convergence studies are given.     

Extended multiscale finite element method for mechanical analysis of heterogeneous materials

An extended multiscale finite element method （EMsFEM） is developed for solving the mechanical problems of heterogeneous materials in elasticity.The underlying idea of the method is to construct numerically the multiscale base functions to capture the small-scale features of the coarse elements in the multiscale finite element analysis.On the basis of our existing work for periodic truss materials, the construction methods of the base functions for continuum heterogeneous materials are systematically introduced. Numerical experiments show that the choice of boundary conditions for the construction of the base functions has a big influence on the accuracy of the multiscale solutions, thus,different kinds of boundary conditions are proposed. The efficiency and accuracy of the developed method are validated and the results with different boundary conditions are verified through extensive numerical examples with both periodic and random heterogeneous micro-structures.Also, a consistency test of the method is performed numerically. The results show that the EMsFEM can effectively obtain the macro response of the heterogeneous structures as well as the response in micro-scale,especially under the periodic boundary conditions.     

Application of stochastic finite element method in estimation of elastic constants for NCF composites

The main aim of this paper is to evaluate the effect of micro-structure variations on elastic constants of NCF (non-crimp fabric) composites. To reach this aim, a three-dimensional unit cell model is developed by the finite element code ABAQUS and mean value of elastic constants in NCF composites are determined by analytical and unit cell based methods with various boundary conditions. In addition, first- and second-order stochastic finite element formulations are derived and variances of elastic constants are computed with respect to the dispersion in length and width of the voids. Results show up to 9.1% scattering in the elastic constants.     

Simulation of metal-forming processes by the finite element method

An algorithm to model the contact, with friction, between a deformable body and rigid surfaces is presented. The method shown is to integrate the equation of motion in the actual reference frame, taking into account the proper constraint set induced by the contact conditions; moreover, the various terms of the 3D stiffness tangent matrix are calculated. The model has been implemented in an FEM code suitable for dealing with finite deformation problems, and the results obtained in the simulation of a bulge-test case and a deep-drawing test are presented and compared with experimental data.     

Large-scale computational fluid dynamics by the finite element method

Solution methods are presented for the large systems of linear equations resulting from the implicit, coupled solution of the Navier-Stokes equations in three dimensions. Two classes of methods for such solution have been studied: direct and iterative methods. For direct methods, sparse matrix algorithms have been investigated and a Gauss elimination, optimized for vector-parallel processing, has been developed. Sparse matrix results indicate that reordering algorithms deteriorate for rectangular, i.e. M × M × N, grids in three dimensions as N gets larger than M. A new local nested dissection reordering scheme that does not suffer from these difficulties, at least in two dimensions, is presented. The vector-parallel Gauss elimination is very efficient for processing on today's supercomputers, achieving execution rates exceeding 2.3 Gflops the Cray YMP-8 and 9.2 Gflops on the NEC on SX3. For iterative methods, two approaches are developed. First, conjugate-gradient-like methods are studied and good results are achieved with a preconditioned conjugate gradient squared algorithm. Convergence of such a method being sensitive to the preconditioning, a hybrid viscosity method is adopted whereby the preconditioner has an artificial viscosity that is gradually lowered, but frozen at a level higher than the dissipation introduced in the physical equations. The second approach is a domain decomposition one in which overlapping domain and side-by-side methods are tested. For the latter, a Lagrange multiplier technique achieves reasonable rates of convergence.     

Transonic viscous-inviscid interaction by a finite element method

A method is outlined for solving two-dimensional transonic viscous flow problems, in which the velocity vector is split into the gradient of a potential and a rotational component. The approach takes advantage of the fact that for high-Reynolds-number flows the viscous terms of the Navier-Stokes equations are important only in a thin shear layer and therefore solution of the full equations may not be needed everywhere. Most of the flow can be considered inviscid and, neglecting the entropy and vorticity effects, a potential model is a good approximation in the flow core. The rotational part of the flow can then be calculated by solution of the potential, streamfunction and vorticity transport equations. Implementation of the no-slip and no-penetration boundary conditions at the walls provides a simple mechanism for the interaction between the viscous and inviscid solutions and no extra coupling procedures are needed. Results are presented for turbulent transonic internal choked flows.     

Modeling and simulation of aerial refueling by finite element method

The aerial refueling hose-and-drogue system is a special case of a generalized aerial cable towed system. The present work investigates the effect of pertinent parameters such as the cable tension, tow point disturbance and vortex wake on the dynamic behavior and stability of the generalized model by using the finite element method with an accurate and computationally efficient three-noded, curved beam element. The analysis results show that the conventional modal and spectrum analysis method is inappropriate for the dynamic stability analysis of the aerial cable towed system. This is because the mechanism of instability due to the tow point disturbance is not the resonance of the aerial cable towed system but the wave propagation downstream along the cable absorbing energy from the airflow when the wave propagation speed is less than the airflow speed. The study also demonstrates that the vortex wake has a significant impact on the dynamics of the aerial cable towed system. The short cable system will orbit with the vortex and the orbiting behavior will diminish as the cable length increases.     

基于有限断裂法和比例边界有限元法的裂纹扩展模拟

基于有限断裂法和比例边界有限元法提出了一种裂缝开裂过程模拟的数值模型。采用基于有限断裂法的混合断裂准则作为起裂及扩展的判断标准,当最大环向应力和能量释放率同时达到其临界值时,裂缝扩展。结合多边形比例边界有限元法,可以半解析地求解裂尖区域附近的应力场和位移场,在裂尖附近无需富集即可获得高精度的解。计算能量释放率时,只需将裂尖多边形内的裂尖位置局部调整,无需改变整体网格的分布,网格重剖分的工作量降至最少。裂缝扩展步长通过混合断裂准则确定,避免了人为假设的随意性,并可以实现裂缝变步长扩展的模拟,更符合实际情况。通过对四点剪切梁的复合型裂缝扩展过程的模拟,对本文模型进行了验证,并应用于重力坝模型的裂缝扩展模拟,计算结果表明,本文提出的模型简单易行且精度较高。     

Displacement fields denoising and strains extraction by finite element method

Optical full-field measurement methods are now widely applied in various domains. In general, the displacement fields can be directly obtained from the measurement, however in mechanical analysis strain fields are preferred. To extract strain fields from noisy displacement fields is always a challenging topic. In this study, a finite element method for smoothing displacement fields and calculating strain fields is proposed. An experimental test case on a holed aluminum specimen under tension is applied to validate this method. The heterogeneous displacement fields are measured by digital image correlation (DIC). By this proposed method, the result shows that the measuring noise on experimental displacement fields can be successfully removed, and strain fields can be reconstructed in the arbitrary area.     

钢筋混凝土板动力非线性有限元研究

从目前的文献看 ,关于钢筋混凝土板动力非线性分析方面的研究较少。本文在建立钢筋混凝土材料动力模型的基础上 ,采用广义协调矩形分层单元、显式 Newmark法编制了钢筋混凝土板的动力有限元程序。数值算例表明 ,所编程序原理正确 ,结果可靠。     

Calculation of quasi-three-dimensional incompressible viscous flows by the finite element method

This paper discusses the calculation of quasi-three-dimensional incompressible viscous flow by FEM. The Reynolds-averaged Navier-Stokes equations are solved in curvilinear co-ordinates by the reduced integration and penalty method (RIP). Streamline upwind artificial viscosity (SUAV) and the Baldwin-Lomax algebraic model of turbulence are used. Time discretization is by the general implicit θ-method.     

FORMING MICHELL TRUSS IN THREE-DIMENSIONS BY FINITEELEMENTMETHOD

IntroductionTheMichell’s[1]theoryforoptimizingstructuraltopologyforstressconstraintsunderoneloadconditionplaysanimportantroleinstructuraloptimizationfield .TheoptimumstructuresbasedonsuchtheoryarecalledasMichelltruss,orleast_weighttruss.Subsequently ,thistheorydevelopedgreatlyinmanyaspects[2 - 8].ItisprovedthatMichelltrussisidenticalwiththeleast_weighttrussforcomplianceconstraints.TheMichelltrussesundersomeloadcasesweregainedbyanalyticalmethod[8- 10 ].Michelltrussisestablishedbasedonstrict…     

The construction of large element in finite element method

In the usual finite element method, the order of the interpolation in an element is kept unchanged, and the accuracy is raised by subdividing the grid denser and denser. Alternatively, in the large element method, the grid is kept unchanged, and the terms of approximate series in the element are increased to raise the accuracy.In this paper, a method for constructing large elements is presented. When using this method, two sets of variables, one set defined inside the element, and the other defined on the boundary of the element, are adopted. Then, these two sets of variables are combined by the hybrid-penalty function method. This method can be applied to any elliptic equations in a domain with arbitrary shape and arbitrary complex boundary condition. It is proved with strict mathematical method in this paper, that in general cases, the accuracy of this method is much higher than that of the usual element and the large element method presented in [7]. Therefore, the degrees of freedom needed in this method are much fewer than those in the two methods if the same accuracy is preserved.     

Stress analysis of weldments by holographic moiré and the finite element method

The research work presented in this paper deals with the determination of the stress concentration at the root of the fillet of a weldment on a T steel specimen. A finite element model was developed for the specimen. Measurements were carried out using the holographic moiré technique. Strain gages were added to evaluate extrapolation techniques proposed in the literature. Good agreement was found between the finite element results and the optically measured values. The strain gage extrapolation technique yielded very low values.     

Postbuckling analysis and imperfection sensitivity of general shells by the finite element method

Buckling and imperfection sensitivity are the primary considerations in analysis and design of thin shell structures. The objective here is to develop accurate and efficient capabilities to predict the postbuckling behavior of shells, including imperfection sensitivity. The approach used is based on the Lyapunov–Schmidt–Koiter (LSK) decomposition and asymptotic expansion in conjunction with the finite element method. This LSK formulation for shells is derived and implemented in a finite element code. The method is applied to cylindrical and spherical shells. Cases of linear and nonlinear prebuckling behavior, coincident as well as non-coincident buckling modes, and modal interactions are studied. The results from the asymptotic analysis are compared to exact solutions obtained by numerically tracking the bifurcated equilibrium branches. The accuracy of the LSK asymptotic technique, its range of validity, and its limitations are illustrated.     

Coarse-graining atomistic dynamics of brittle fracture by finite element method

In this work we present the finite element (FE) implementation of an atomistic formulation of balance equations and its application to coarse-grained (CG) simulation of dynamic fracture. First, we simulate a notched specimen that contains about 1.8 million atoms by the CG-FE method, and we compare the CG-FE results with that by all-atom molecular dynamics (MD) simulations. We find that CG-FE simulations with about 5% degrees of freedom of the MD simulation can capture the essential dynamic features, not in exact correspondence, but qualitatively and quantitatively similar to that obtained by MD simulations. We then proceed to simulate a series of micron-sized specimens by the CF-FE method. We find that it is the interaction of the forward propagating crack with the stress waves being reflected back by the boundaries of the specimen that triggers the dynamic instability and hence the branching of cracks in micron-sized specimens. The potential application of the method and future work for improvements are discussed.     

On vibration of hemispherical shell by using finite element method

This paper establishes the finite element equation for the spherical shell.The resonantfrequencies of the above shell under different boundary conditions are also discussed andcalculated.     

Numerical analysis of one-dimensional nonlinear large-strain consolidation by the finite element method

The nonlinear partial differential equation model of Gibson et al. which governs one-dimensional large-strain consolidation is solved numerically using a semi-discrete formulation involving a Galerkin weighted residual approach. The use of quadratic Lagrange basis functions usually complicates the task of solving the system of time-dependent ordinary differential equations that are obtained with the semi-discrete Galerkin procedure. However, an efficient algorithm has been discovered yielding the advantages of quadratic interpolation without undue computational burden.Although considerable effort has already been made to solve the PDE of large-strain consolidation by numerical methods, a satisfactory set of benchmarks is still needed to assess accuracy. To fill this need, three procedures are reported which allow numerical solutions of the large-strain model to be reliably evaluated. One involves the use of perturbation methodology to provide a solution when only self-weight effects are present. A second utilizes an analytical solution developed by Philip when self-weight effects are absent and the third involves the exact calculation of the discharge flux through the upper boundary of a deposit consolidating through self-weight effects alone. All three are restricted to early-time consolidation and are illustrated in the context of the finite element method.