Finite Element Analysis to Two-Dimensional Nonlinear Sloshing Problems

A two-dimensional nonlinear sloshing problem is analyzed by means of the fully nonlinear theory and time domain second order theory of water waves. Liquid sloshing in a rectangular container Subjected to a horizontal excitation is simulated by the finite element method. Comparisons between the two theories are made based on their numerical results. It is found that good agreement is obtained for the case of small amplitude oscillation and obvious differences occur for large amplitude excitation. Even though, the second order solution can still exhibit typical nonlinear features of nonlinear wave and can be used instead of the fully nonlinear theory.

A Numerical Algorithm Based on Quadratic Finite Element for Two-Dimensional Nonlinear Time Fractional Thermal Diffusion Model

In this article,a high-order scheme,which is formulated by combining the quadratic finite element method in space with a second-order time discrete scheme,is developed for looking for the numerical solution of a two-dimensional nonlinear time fractional thermal diffusion model.The time Caputo fractional derivative is approximated by using the L2-1formula,the first-order derivative and nonlinear term are discretized by some second-order approximation formulas,and the quadratic finite element is used to approximate the spatial direction.The error accuracy O(h3+
t2)is obtained,which is verified by the numerical results.

COMPACTLY SUPPORTED NON-TENSOR PRODUCT FORM TWO-DIMENSION WAVELET FINITE ELEMENT

Some theorems of compactly supported non-tensor product form two-dimension Daubechies wavelet were analysed carefully. Compactly supported non-tensor product form two-dimension wavelet was constructed, then non-tensor product form two dimension wavelet finite element was used to solve the deflection problem of elastic thin plate. The error order was researched. A numerical example was given at last.

RELIABILITY OF ELASTO-PLASTIC STRUCTURE USING FINITE ELEMENT METHOD

A solution of probabilistic FEM for elastic-plastic materials is presented based on the incremental theory of plasticity and a modified initial stress method. The formulations are deduced through a direct differentiation scheme. Partial differentiation of displacement, stress and the performance function can be iteratively performed with the computation of the mean values of displacement and stress. The presented method enjoys the efficiency of both the perturbation method and the finite difference method, but avoids the approximation during the partial differentiation calculation. In order to improve the efficiency, the adjoint vector method is introduced to calculate the differentiation of stress and displacement with respect to random variables. In addition, a time-saving computational method for reliability index of elastic-plastic materials is suggested based upon the advanced First Order Second Moment (FOSM) and by the usage of Taylor expansion for displacement. The suggested method is also applicable to 3-D cases.

Numerical Simulation and Experimental Studies on Elastic-Plastic Fatigue Crack Growth

A elastic-plastic fatigue crack growth(FCG)finite element model was developed for predicting crack growth rate under cyclic load.The propagation criterion for this model was established based on plastically dissipated energy.The crack growth simulation under cyclic computation was implemented through the ABAQUS scripting interface.The predictions of this model are in good agreement with the results of crack propagation experiment of compact tension specimen made of 304 stainless steel.Based on the proposed model,the single peak overload retardation effect of elastic-plastic fatigue crack was analyzed.The results shows that the single peak overload will reduce the accumulation rate of plastic energy dissipation of elements at crack tip plastic zone,so that crack growth will be arrested.The crack growth rate will not recover until the crack tip exceed the affected region.Meanwhile,the crack growth rate is mainly determined by the amplitude rather than the mean load under the condition of small scale yielding.The proposed model would be helpful for predicting the growth rate of mode I elastic-plastic fatigue crack.

Analysis of the elastic-plastic indentation properties of materials with varying ratio of hardness to Young’s modulus

The elastic-plastic indentation properties of materials with varying ratio of hardness to Young’s modulus(H/E) were analyzed with the finite element method. And the indentation stress fields of materials with varying ratio H/E on the surface were studied by the experiment. The results show that the penetration depth, contact radius, plastic pile-up and the degree of elastic recovery depend strongly on the ratio H/E. Moreover, graphs were established to describe the relationship between the elastic-plastic indentation parameters and H/E. The established graphs can be used to predict the H/E of materials when compared with experimental data.

A NEW NUMERICAL SCHEME FOR ELASTIC-PLASTIC SIMULATION OF EXCAVATION IN GEO-ENGINEERING

For the path dependency and nonlinearity introduced by incremental construction, numerical method has been widely used in deformation analysis of geo engineering.In the numerical simulation scheme commonly used in the past, the excavating loads are extracted from nodal stresses, which are deduced linearly from the stresses at Gauss point in finite element method.The unneglectable calculation error is contained in this process when elastic plastic constitutive model is employed.The error mentioned above is analyzed in detail.Based on the analysis of excavation process and the principle of finite element theory, a new simulation scheme for excavation is proposed.At the end of this paper, an application in rock engineering is given out.

AN IMPROVED EFFICIENT SEMI-IMPLICIT FINITE ELEMENT SCHEME FOR TWO-DIMENSIONAL TIDAL FLOW COMPUTATIONS

In a recent paper, an efficient semi-implicit finite element scheme for 2-dimensional tidal flow computations is proposed. In that scheme, each term of the governing equations, rather than each dependent variable, is ex- panded in terms of the unknown nodal values. Simpson's rule ix used for numerical integration to make the mass matrix diagonal. The friction terms are represented semi-implicitly to improve stability, but no additional compu- tational effort is required. The shortcomings of this scheme are that the time-stepping scheme is only first-order ae- curate and artificial smoothing is required to control the numerical noise. In this paper, the previous scheme is im- proved by including the eddy viscosity terms in the governing equations to replace artificial smoothing in noise con- trol and the time-stepping scheme is modified to make it second-order accurate. These improvements can be achieved with only a slight increase in computational effort. The test cases used previously to validate the former scheme are again employed to test the present scheme.

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.

Structural characteristics of cement-stabilized soil bases with 3D finite element method

Cement-stabilized soil bases have been widely used in expressways due to its high strength,appropriate stiffness,good water resistance,and frost resistance.So far,the structural characteristics and mechanical behaviors of cement-stabilized soil bases were not investigated so much.In this paper,the 3D elastic-plastic finite element method(FEM)was used to analyze the mechanical behaviors and structural characteristics of cementstabilized soil bases from construction to operation.The pavement filling and the traffic loading processes were simulated,and a contact model was used to simulate the contact behavior between each layer of the pavement.Considering the construction process,the structural characteristics and mechanical behaviors of cementstabilized soil bases were studied under asphalt-concrete pavement conditions.Furthermore,the general rules of deformations and stresses in cement-stabilized soil bases under different conditions were discussed,and some suggestions were put forward for the design and construction of cement-stabilized soil bases.

Temperature field analysis and its application in hot continuous rolling of Inconel 718 superalloy

A coupled thermo-mechanical model containing metal flow and temperature field for calculating temperature variation has been developed on fourteen-pass hot continuous rolling of round rod for Inconel 718 alloy using 3D elastic-plastic finite element method （FEM）. The temperature of characteristic analysis points in the intermediate cross-section of the workpiece has been simulated at initial temperature ranging from 960 to 1000 ℃ and initial velocity in range of 0.15-0.55 m·s^-1. Based on finite element analysis and microstructural observation in cylindrical hot compression experiments, the appropriate hot continuous rolling technologies have been designed for rod products with different diameters. For a real rolling practice, the simulated surface temperature was examined and is in good agreement with the measured one.

Numerical Study of the Plastic Behaviour of a Low Alloy Steel during Phase Transformation

Phase transformations in steels play a major role on the generation of residual stresses and distortions during thermal processes such as welding and heat treatments. In this paper, we focus on the influence of phase transformations on the plastic behaviour of a low-alloy steel. It is now well known that the plastic strain rate can then be decomposed as the sum of two terms. The first one corresponds to classical plasticity while the second one is due to the evolution of the transformation and is usually referred to as corresponding to transformation induced plasticity. A theoretical approach of the problem has been achieved ([1][2][3]] and a macroscopic model has been proposed in the case of ideal-plastic phases. The theoretical approach has been assessed and completed using micromechanical numerical simulations but these were based on rather coarse 3D meshes due to limited computer capabilities in the 80’s. This paper presents new finite element micromechanical calculations using refined meshes to analyse the classical plastic behaviour and transformation induced plasticity. The results of the computations are discussed and compared with the calculations initially performed. Finally improvements of the macroscopic model are proposed.

Temperature-dependent constitutive modeling of a magnesium alloy ZEK100 sheet using crystal plasticity models combined with in situ high-energy X-ray diffraction experiment

A multiscale crystal plasticity model accounting for temperature-dependent mechanical behaviors without introducing a larger number of unknown parameters was developed.The model was implemented in elastic-plastic self-consistent(EPSC)and crystal plasticity finite element(CPFE)frameworks for grain-scale simulations.A computationally efficient EPSC model was first employed to estimate the critical resolved shear stress and hardening parameters of the slip and twin systems available in a hexagonal close-packed magnesium alloy,ZEK100.The constitutive parameters were thereafter refined using the CPFE.The crystal plasticity frameworks incorporated with the temperature-dependent constitutive model were used to predict stress–strain curves in macroscale and lattice strains in microscale at different testing temperatures up to 200℃.In particular,the predictions by the crystal plasticity models were compared with the measured lattice strain data at the elevated temperatures by in situ high-energy X-ray diffraction,for the first time.The comparison in the multiscale improved the fidelity of the developed temperature-dependent constitutive model and validated the assumption with regard to the temperature dependency of available slip and twin systems in the magnesium alloy.Finally,this work provides a time-efficient and precise modeling scheme for magnesium alloys at elevated temperatures.

NUMERICAL SIMULATION OF HOT SAWING PROCESS

The present paper gives a numerical simulation of hot sawing process by using elastic- plastic finite element method. The simulation is carried out for the moment from the beginning of deformation to the local yield in work piece. In order to treat the work hardening on deformation resistance, a correction of stress based on deformation rate is taken into consideration. The calculation results shows, there are two stress peaks both on the lower and upper sides ahead of the tooth tip during the elastic press stage, in which the displacement of tooth is below 0.735*10-6 cm. Following the push of saw tooth and rise of saw load, metal at the corner of filing reaches the yield point and a local plastic area appears,where metal shapes new filing part towards the free surface under the extrusion forces. Meanwhile the stress peaks ahead of tooth tip initial also yield regions. The displacement of saw tooth is between 0.735*10-6cm and 1.274*10-6cm in this stage. With the further push of the saw tooth, metal bounded to tooth tip is torn under the combination of tensile and sheer stress. The slide of metal and its local plastic flow form the extension of filing. Then the saw load rises no longer and static sawing procedure continues.

Analysis of effect factors on crack rotation factor

Crack rotation factor r and plastic crack rotation factor rp are analyzed by means of simulated test using finite element methods. The results indicate that r and rp are influenced by material and geometry parameters in three-point bend specimen and r and rp are variable value in small scope of yield. Therefore, it has some great error that r and rp are regarded as constants in analyzing CTOD crack driving force.

Analysis of mechanical strengths of extreme line casing joint considering geometric, material, and contact nonlinearities

To address the challenges associated with difficult casing running,limited annular space,and poor cementing quality in the completion of ultra-deep wells,the extreme line casing offers an effective solution over conventional casings.However,due to its smaller size,the joint strength of extreme line casing is reduced,which may cause failure when running in the hole.To address this issue,this study focuses on the CST-ZTΦ139.7 mm×7.72 mm extreme line casing and employs the elastic-plastic mechanics to establish a comprehensive analysis of the casing joint,taking into account the influence of geometric and material nonlinearities.A finite element model is developed to analyze the forces and deformations of the extreme line casing joint under axial tension and external collapse load.The model investigates the stress distribution of each thread tooth subjected to various tensile forces and external pressures.Additionally,the tensile strength and crushing strength of the extreme line casing joint are determined through both analytical and experimental approaches.The findings reveal that,under axial tensile load,the bearing surface of each thread tooth experiences uneven stress,with relatively high equivalent stress at the root of each thread tooth.The end thread teeth are valuable spots for failure.It is observed that the critical fracture axial load of thread decreases linearly with the increase of thread tooth sequence.Under external pressure,the circumferential stress is highest at the small end of the external thread,leading to yield deformation.The tensile strength of the joint obtained from the finite element model exhibits a relative error of less than 7%compared to the analytical and experimental values,proving the reliability of the finite element model.The tensile strength of the joint is 3091.9 k N.Moreover,in terms of anti-collapse capability,the joints demonstrate higher resistance to collapse compared to the casing body,which is consistent with the test results where the pipe body experiences collapse and failure while the joints remain intact during the experiment.The failure load of the casing body under external collapse pressure is 87.4 MPa.The present study provides a basic understanding of the mechanical strengths of extreme line casing joint.

New formula for predicting the plastic buckling pressure of steel torispherical heads under internal pressure

Thin-walled torispherical heads under internal pressure can fail by plastic buckling because of compressive circumferential stresses in the head knuckle.However,existing formulas still have limitations,such as complicated expressions and low accuracy,in determining buckling pressure.In this paper,we propose a new formula for calculating the buckling pressure of torispherical heads based on elastic-plastic analysis and experimental results.First,a finite element(FE)method based on the arc-length method is established to calculate the plastic buckling pressure of torispherical heads,considering the effects of material strain hardening and geometrical nonlinearity.The buckling pressure results calculated by the FE method in this paper have good consistency with those of BOSOR5,which is a program for calculating the elastic-plastic bifurcation buckling pressure based on the finite difference energy method.Second,the effects of geometric parameters,material parameters,and restraint form of head edge on buckling pressure are investigated.Third,a new formula for calculating plastic buckling pressure is developed by fitting the curve of FE results and introducing a reduction factor determined from experimental data.Finally,based on the experimental results,we compare the predictions of the new formula with those of existing formulas.It is shown that the new formula has a higher accuracy than the existing ones.