Fracture analysis of rock mass based on 3-D nonlinear Finite Element Method

Traditional fracture analysis is based on fracture mechanics and damage mechanics. They focus on the propagation of the fracture. However, their propagation criterions are not easily applied in practice and the current analysis is limited in planar problem. This paper presents a new theory that the occurrence of the unbalanced force (derived from the Deformation Reinforcement Theory) could be the criterion of the initiation of the fracture, and the distribution area and propagation of the unbalanced force could be the indication of the fracture propagation direction. By aggregate analysis with Stress Intensity Factor (SIF) criterion, the unbalanced force actually is the opposite external load that is the SIF difference incurred between the external loads and permitted by the structure. Numerical simulation and physical experiments on pre-fracture cuboid rock specimens proved that the occurrence of the unbalanced force could be the initiation of the fracture. Mesh size dependence was also considered by analysis of different mesh size finite element gravity dam models. Furthermore, the theory was applied to the feasibility analysis of the Baihetan arch dam together with physical experiments in order to evaluate the fracture propagation of dam heel. The results show that it is an effective way to use unbalanced force to analyze the fracture initiation and propagation when performing 3-dimensional nonlinear FEM calculation.

Nonlinear Finite Element Method Considering Martensite Plasticity for Shape Memory Alloy Structure

This work presents a nonlinear finite element method to simulate the macroscopic mechanical responses and the effects of martensite plasticity in a shape memory alloy(SMA)structure.A linear relationship formulation is adopted to express the influence of martensite plasticity on the inverse martensitic phase transition of SMA material.Incorporating with a trigonometric-type phase transition evolution law and an exponential-type plastic flow evolution law,an incremental mechanical model with two internal variables is supposed based on the macroscopic experimental phenomena.A nonlinear finite element equation is formulated and solved by the principle of virtual displacement and Newton-Raphson method respectively.By employing the proposed nonlinear finite element method,the uniform tensile bar and three-point bending beam are simulated and analyzed.Results illustrate that the presented nonlinear finite element method is suitable to act as an effective computational tool for the wide applications based on the SMA material considering the effects of martensite plasticity because all material constants related to the method can be obtained from macroscopic experiments.

Full－range nonlinear analysis of fatigue behaviors of reinforced concrete structures by finite element method

The offshore reinforced concrete structures are always subject to cyclic load, such as wave load.In this paper a new finite element analysis model is developed to analyze the stress and strain state of reinforced concrete structures including offshore concrete structures, subject to any number of the cyclic load. On the basis of the anal ysis of the experimental data,this model simplifies the number of cycles-total cyclic strain curve of concrete as three straight line segments,and it is assumed that the stress-strain curves of different cycles in each segment are the same, thus the elastoplastic analysis is only needed for the first cycle of each segment, and the stress or strain corresponding to any number of cycles can be obtained by superposition of stress or strain obtained by the above e lastoplastic analysis based on the cyclic numbers in each segment.This model spends less computer time,and can obtain the stress and strain states of the structures after any number of cycles.The endochronic-damage and ideal offshore concrete platform subject to cyclic loading are experimented and analyzed by the finite element method based on the model proposed in this paper. The results between the experiment and the finite element analysis are in good agreement,which demonstrates the validity and accuracy of the proposed model.

Finite Element Method Based on Equivalent Magnetic Energy Method for Computation of 2D Nonlinear Eddy Current Field

In this paper, the finite element method using vector potential in applications to 2D nonlinear eddy current field is discussed. The authors use the equivalent magnetic energy method to deal with magnetization curve of ferromagnetic material,and present the formulation of 2D nonlinear eddy current field.With this method the authors analyze the eddy current field in an induction ladle furnace and the force distribution in the charge (molten metal),and plot the corresponding curves.

Finite element analyses of Wanjiazhai water transmission tunnel excavation and service

This paper is devoted to the nonlinear stress and strain analysis oftunneling and working conditions of Wanjiazhai Division Project No.7 Tunnel in Shanxi province ofChina. The initial geological stress of loess was simulated by grading fill; the theory of unloadingproposed by Duncan and boundary stress of elasticity were used to calculate the excavation of thetunnel; Goodman joint elements were applied to simulate the joints of the liners; both loading andunloading tests have been performed to determine the parameters of Duncan-Chang's model and thecalculated results were compared; Terzaghi' s theory on loosening earth pressure was applied. Manyworking conditions were analyzed and some reasonable results were obtained. Based on the analyses,reparative measures were proposed and completed. The tunnel has functioned well since October, 2001.

Arc-length technique for nonlinear finite element analysis

Nonlinear solution of reinforced concrete structures, particularly complete load-deflection response, requires tracing of the equilibrium path and proper treatment of the limit and bifurcation points. In this regard, ordinary solution techniques lead to instability near the limit points and also have problems in case of snap-through and snap-back. Thus they fail to predict the complete load-displacement response. The arc-length method serves the purpose well in principle, received wide acceptance in finite element analysis, and has been used extensively. However modifications to the basic idea are vital to meet the particular needs of the analysis. This paper reviews some of the recent developments of the method in the last two decades, with particular emphasis on nonlinear finite element analysis of reinforced concrete structures.

Finite Element Analysis on Plane Stress Crack Growth in a Power-Law Hardening Material

Aim To determine numerically the field characteristics in the vied at the tip of a place crack growing steadily in a power-law hardening material. Meteods. Methods on the Euler mode and small-scale yield assumption, the numerical results were given by nonlinear finite element analysis. Results The numerical results of the shape of the active plastic sone, the angular distribution of stresseses and Clack tip opening displacement (CTOD) in the vicinity at the hp of the steadily groWing CraCk are determined. Conclusion The comparison between the numerical results given by the present wort and those given by analytic asymptotic analysis shows that the present work reached a very high accuracy.

Nonlinear static response of piezoelectric plates considering electro-mechanical coupling

Nonlinear static analysis of piezoelectric plates has been carried out using nonlinear finite element method considering electro-mechanical coupling,The geometrical nonlinearity has been taken into account and electric potential is assumed to be quadratic across the plate thickness,The governing equations are obtained using potential energy and Hamilton's principle that includes elastic and piezoelectric effects.The finite element model is derived based on constitutive equation of piezoelectric material accounting for coupling between elasticity and electric effect using higher order plate elements,Results are presented for piezoelectric plate under different mechanical boundary conditions,Numerical results for the plate are given in dimensionless graphical forms.Effects of boundary conditions on linear and nonlinear response of the plate are also studied.The numerical results obtained by the present model are in good agreement with the available solutions reported in the literature.

Verification of Seismic Performance of Pile Foundation in Composite Ground through Experimental and Numerical Methods

A new construction method of pile foundation in composite ground, in which, prior to installing piles, the ground is improved around the heads of the piles in soft ground or ground subject to liquefaction, which is introduced in this paper. This construction method uses a combination of pile foundation construction together with common ground improvement methods, including deep mixing, preloading and sand compaction piling, and it is referred to as the composite ground pile method. Since an artificial ground with relatively high rigidity comparing with that of the original ground was formed around the pile in this method, and the seismic performance has not been made clear, thus the seismic performance of piles in composite ground was systematically analyzed through a series of centrifuge model tests and numerical analyses by using dynamic nonlinear finite element method, and a verification method for the seismic performance of piles in composite ground was proposed on the basis of the experimental and numerical results.

TWO-DIMENSIONAL FINITE ELEMENT METHOD FOR DETERMINING NONLINEAR WAVE FORCES ON LARGE SUBMERGED BODIES

In this paper, we first develop the far field asymptotic solutions of the second-order scattering waves for the vertical plane problem taking the second-order Stokes waves as the incident waves. The asymptotic solutions satisfy the Laplace equation, the sea bed and free surface boundary conditions and are the out-going waves. Then the radiation conditions of the second-order mattering waves are derived by using the asymptotic solutions. By using the two-dimensinal finite clement method with the radiation conditions imposed on the ar- tificial boundaries, the computer program, known as 'NWF2', for determining nonlinear wave forces on large submerged bodies has been written. As a numerical example, nonlinear wave forces on a semi-circu- lar cylinder lying on the sea bed arc presented.

裂纹加筋和缺口加筋对钢加筋板极限强度的影响

This paper numerically evaluates the effect of the crack position on the ultimate strength of stiffened panels.Imperfections such as notches and cracks in aged marine stiffened panels can reduce their ultimate strength.To investigate the effect of crack length and position,a series of nonlinear finite element analyses were carried out and two cases were considered,i.e.,case 1 with thin stiffeners and case 2 with thick stiffeners.In both cases,the stiffeners have the same cross-section area.To have a basis for comparison,the intact panels were modeled as well.The cracks and notches were in the longitudinal and transverse direction and were assumed to be in the middle part of the panel.The cracks and notches were assumed to be through the thickness and there is neither crack propagation nor contact between crack faces.Based on the numerical results,longitudinal cracks affect the behavior of the stiffened panels in the postbuckling region.When the stiffeners are thinner,they buckle first and provide no reserved strength after plate buckling.Thus,cracks in the stiffeners do not affect the ultimate strength in the case of the thinner stiffeners.Generally,when stiffeners are thicker,they affect the postbuckling behavior more.In that case,cracks in the stiffeners affect the buckling and failure modes of the stiffened panels.The effect of notch was also studied.In contrast to the longitudinal crack in stiffeners,a notch in the stiffeners reduces the ultimate strength of the stiffened panel for both slender and thick stiffeners.

Characteristic Verification and Parameter Optimization of Airbags Cushion System for Airborne Vehicle

Abstract： The major methods to investigate the airbags cushion system are experimental method, thermodynamic method and finite element method （FEM）. Airbags cushion systems are very complicated and very difficult to be investigated thoroughly by such methods For experimental method, it is nearly impossible to completely analyze and optimize the cushion characteristics of airbags of airborne vehicle because of charge issue, safety concern and time constraint. Thermodynamic method fails to take the non-linear effects of large airbag deformation and varied contact conditions into consideration. For finite element method, the FE model is usually complicated and the calculation takes tens of hours of CPU time. As a result, the optimization of the design based on a nonlinear model is very difficult by traditional iterative approach method. In this paper, a model based on FEM and control volume method is proposed to simulate landing cushion process of airborne vehicle with airbags cushion system in order to analyze and optimize the parameters in airbags cushion system. At first, the performance of airbags cushion system model is verified experimentally. In airdrop test, accelerometers are fixed in 4 test points distributed over engine mount, top, bottom and side armor plate of hull to obtain acceleration curves with time. The simulation results are obtained under the same conditions of the airdrop test and the simulation results agree very well with the experimental results, which indicate the established model is valid for further optimization. To optimize the parameters of airbags, equivalent response model based on Latin Hypercube DOE and radial basis function is employed instead of the complex finite element model. Then the optimal results based on equivalent response model are obtained using simulated annealing algorithm. After optimization, the maximal acceleration of airborne vehicle landing reduces 19.83%, while the energy absorption by airbags increases 7.85%. The performance of the airbags cushion system thus is largely improved through optimization, which indicates the proposed method has the capability of solving the parameter optimization problem of airbags cushion system for airborne vehicle.

ANALYSIS OF DAMAGE NEAR A CONDUCTING CRACK IN A PIEZOELECTRIC CERAMIC

The finite element formulation for analyzing static damage near a conducting crack in a thin piezoelectric plate is established from the virtual work principle of piezoelectricity.The damage fields under various mechanical and electrical loads are calculated carefully by using an effective iterative procedure.The numerical results show that all the damage fields around a crack tip are fan-shaped and the electric field applied has great influence on the mechanical damage, which is related to the piezoelectric properties.

Performance index limits of high reinforced concrete shear wall components

The deformation performance index limits of high reinforced concrete （RC） shear wall components based on Chinese codes were discussed by the nonlinear finite element method. Two typical RC shear wall specimens in the previous work were first used to verify the correctness of the nonlinear finite element method. Then, the nonlinear finite element method was applied to study the deformability of a set of high RC shear wall components designed according to current Chinese codes and with shear span ratio λ≥2.0. Parametric studies were made on the influence of shear span ratio, axial compression ratio, ratio of flexural capacity to shear capacity and main flexural reinforcement ratio of confined botmdary members. Finally, the deformation performance index and its limits of high RC shear wall components under severe earthquakes were proposed by the finite element model results, which offers a reference in determining the performance status of RC shear wall components designed based on Chinese codes.

h-P Finite Element Approximation for Full-Potential Electronic Structure Calculations

The(continuous) finite element approximations of different orders for the computation of the solution to electronic structures were proposed in some papers and the performance of these approaches is becoming appreciable and is now well understood.In this publication,the author proposes to extend this discretization for full-potential electronic structure calculations by combining the refinement of the finite element mesh,where the solution is most singular with the increase of the degree of the polynomial approximations in the regions where the solution is mostly regular.This combination of increase of approximation properties,done in an a priori or a posteriori manner,is well-known to generally produce an optimal exponential type convergence rate with respect to the number of degrees of freedom even when the solution is singular.The analysis performed here sustains this property in the case of Hartree-Fock and Kohn-Sham problems.