A quadrilateral membrane hybrid stress element with drilling degrees of freedom

A new kind of quadrilateral assumed stress hy- brid membrane element with drilling degrees of freedom and a traction-free inclined side has been developed based on an extended Hellinger-Reissner principle which is established by expanding the essential terms of the assumed stress field as polynomials in the natural coordinates of the element. The homogeneous equilibrium equations are imposed in a variational sense through the internal displacements which are also expanded in the natural coordinates, while the tractionfree conditions along the inclined side are satisfied exactly. The use of such special element in the finite element solution is shown to be highly accurate when only a very coarse element mesh is used for plates with V-shaped rounded notches or inclined sides.

A hybrid-stress element based on Hamilton principle

A novel hybrid-stress finite element method is proposed for constructing simple 4-node quadrilateral plane elements, and the new element is denoted as HH4-3fl here. Firstly, the theoretical basis of the traditional hybrid-stress elements, i.e., the Hellinger-Reissner variational principle, is replaced by the Hamilton variational principle, in which the number of the stress variables is reduced from 3 to 2. Secondly, three stress parameters and corresponding trial functions are introduced into the system equations. Thirdly, the displacement fields of the conventional bilinear isoparametric element are employed in the new models. Finally, from the stationary condition, the stress parameters can be expressed in terms of the displacement parameters, and thus the new element stiffness matrices can be obtained. Since the required number of stress variables in the Hamilton variational principle is less than that in the Hellinger-Reissner variational principle, and no additional incompatible displacement modes are considered, the new hybrid-stress element is simpler than the traditional ones. Furthermore, in order to improve the accuracy of the stress solutions, two enhanced post-processing schemes are also proposed for element HH4-3β. Numerical examples show that the proposed model exhibits great improvements in both displacement and stress solutions, implying that the proposed technique is an effective way for developing simple finite element models with high performance.

Orthogonal basic deformation mode method for zero-energy mode suppression of hybrid stress elements

A set of basic deformation modes for hybrid stress finite elements are directly derived from the element displacement field. Subsequently, by employing the so-called united orthogonal conditions, a new orthogonalization method is proposed. The result- ing orthogonal basic deformation modes exhibit simple and clear physical meanings. In addition, they do not involve any material parameters, and thus can be efficiently used to examine the element performance and serve as a unified tool to assess different hybrid elements. Thereafter, a convenient approach for the identification of spurious zero-energy modes is presented using the positive definiteness property of a flexibility matrix. More- over, based on the orthogonality relationship between the given initial stress modes and the orthogonal basic deformation modes, an alternative method of assumed stress modes to formulate a hybrid element free of spurious modes is discussed. It is found that the orthogonality of the basic deformation modes is the sufficient and necessary condition for the suppression of spurious zero-energy modes. Numerical examples of 2D 4-node quadrilateral elements and 3D 8-node hexahedral elements are illustrated in detail to demonstrate the efficiency of the proposed orthogonal basic deformation mode method.

THE STRESS SUBSPACE OF HYBRID STRESS ELEMENT AND THE DIAGONALIZATION METHOD FOR FLEXIBILITY MATRIX H

The following is proved: 1) The linear independence of assumed stress modes is the necessary and sufficient condition for the nonsingular flexibility matrix; 2) The equivalent assumed stress modes lead to the identical hybrid element. The Hilbert stress subspace of the assumed stress modes is established. So, it is easy to derive the equivalent orthogonal normal stress modes by Schmidt's method. Because of the resulting diagonal flexibility matrix, the identical hybrid element is free from the complex matrix inversion so that the hybrid efficiency, is improved greatly. The numerical examples show that the method is effective.

Interface stress element method and its application in analysis of anti-sliding stability of gravity dam

The rigid body limit equilibrium method （LEM） and the nonlinear finite element method （NFEM） are often used in the analysis of anti-sliding stability of gravity dam. But LEM cannot reflect the process of progressive instability and mechanical mecha- nism on failure for rock mass while NFEM is difficult to use to solve the displacement discontinuity of weak structural plane. Combining the research with Xiangjiaba Hydropower Station project, the analysis of anti-sliding stability for segment 12# of the dam has been carried out using interface stress element method （ISEM）. The results can reflect the most dangerous location, the scope and distribution of failure zone in weak structural plane, and present the process of progressive failure in dam foun- dation as well as the safety coefficient of possible sliding body. These achievements provide an important technical reference for dam foundation treatment measures. The computational results show that ISEM can naturally describe discontinuous de- formation of rock mass such as dislocation, openness and sliding. Besides, this method is characterized by good adaptability, convenient calculation and high compatibility, thus it is regarded as an effective way to make an analysis of anti-sliding stabil- ity of gravity dam

DEFORMATION RIGIDITY OF ASSUMED STRESS MODES IN HYBRID ELEMENTS

The new methods to determine the zero-energy deformation modes in the hybrid elements and the zero-energy stress modes in their assumed stress fields are presented by the natural deformation modes of the elements. And the formula of the additional element deformation rigidity due to additional mode into the assumed stress field is derived. Based on, it is concluded in theory that the zero-energy stress mode cannot suppress the zero-energy deformation modes but increase the extra rigidity to the nonzero-energy deformation modes of the element instead. So they should not be employed to assume the stress field. In addition, the parasitic stress modes will produce the spurious parasitic energy and result the element behaving over rigidity. Thus, they should not be used into the assumed stress field even though they can suppress the zero-energy deformation modes of the element. The numerical examples show the performance of the elements including the zero-energy stress modes or the parasitic stress modes.

A New Hybrid Stress Element with Fluid

In the process of shale gas exploitation,there exits two difficult problems:one is the real numerical simulation of a tremendous number of holes in actual shale;the other is the fluid–solid coupling problem involved in holes,where the difficulty of transition at the interface between the Eulerian grid and the Lagrangian grid becomes the most important.In response to these two problems,this paper establishes an element model with both fluid and solid.At the fluid–solid interface,the equilibrium condition of the surface force is introduced to obtain the modified complementary energy functional,and a new hybrid stress element with fluid is derived.The comparison of the simulation results with those of the ordinary commercial finite element software verifies the effectiveness and efficiency of this element,and proves its applicability in the problem of shale with numerous holes.Furthermore,this element can be extended to general problems of solid with fluid in.

A New Classification Method of Stress Modes in Hybrid Stress Finite Element

The paper presents a new method for classifying the stress modes in hybrid stress finite element in terms of natural stress modes in finite element and the rank analysis of matrix G in forming element It reveals the relation among the different assumed stress field, and gives the general method in forming stress field Comparing with the method of eigenvalue analysis, the new method is more efficient

Special hybrid stress element for stress analyses around circular cutouts in laminated composites

A 3-dimensional hybrid stress element with a traction-free cylindrical surface based on amodified complementary energy principle has been derived for efficient and accurate analysis of stressconcentration around circular cutouts in thin to thick laminated composites. New expressions of sixstress components are developed by using three stress-functions in cylindrical co-ordinates, so that thehomogeneous equilibrium equations, the interlayer surface transverse-stresses and the traction-freeboundary condition on the cylindrical surface are satisfied exactly, while the interelement traction conti-nuity has been relaxed via the Lagrange multiplier method. Transverse-shear deformation effects areincorporated in each layer with displacement continuity enforced along interlayer surface. Selected ex-amples are used to demonstrate the efficiency and accuracy of the present special element.

3-D FINITE ELEMENT ANALYSIS OF THE EFFECT OF WELDING RESIDUAL STRESS ON HYDROGEN DIFFUSION IN HYDROGEN CONTAINED ENVIRONMENT

The hydrogen distribution of 16MnR steel weldment in hydrogen contained environment was calculated using the finite element method （ FEM）. The effect of welding residual stress on hydrogen diffusion has been discussed using a 3-D sequential coupling finite element analysis procedure complied by Abaqus code. The hydrogen diffusion coefficient in weld metal, the heat affected zone （HAZ）, and the base metal of the 16MnR steel weldment were measured using the electrochemical permeation technique. The hydrogen diffusion without the effect of stress was also calculated and compared. Owing to the existence of welding residual stress, the hydrogen concentration was obviously increased and the hydrogen wouM diffuse and accumulate in the higher stress region.

COMPUTATION OF SUPER-CONVERGENT NODAL STRESSES OF TIMOSHENKO BEAM ELEMENTS BY EEP METHOD

The newly proposed element energy projection(EEP) method has been applied to the computation of super_convergent nodal stresses of Timoshenko beam elements.General formulas based on element projection theorem were derived and illustrative numerical examples using two typical elements were given.Both the analysis and examples show that EEP method also works very well for the problems with vector function solutions.The EEP method gives super_convergent nodal stresses,which are well comparable to the nodal displacements in terms of both convergence rate and error magnitude.And in addition,it can overcome the “shear locking” difficulty for stresses even when the displacements are badly affected.This research paves the way for application of the EEP method to general one_dimensional systems of ordinary differential equations.

Determination of stress intensity factor with direct stress approach using finite element analysis

In this article, a direct stress approach based on finite element analysis to determine the stress intensity factor is improved. Firstly, by comparing the rigorous solution against the asymptotic solution for a problem of an infinite plate embedded a central crack, we found that the stresses in a restrictive interval near the crack tip given by the rigorous solution can be used to determine the stress intensity factor, which is nearly equal to the stress intensity factor given by the asymptotic solution. Secondly, the crack problem is solved numerically by the finite element method. Depending on the modeling capability of the software, we designed an adaptive mesh model to simulate the stress singularity. Thus, the stress result in an appropriate interval near the crack tip is fairly approximated to the rigorous solution of the corresponding crack problem. Therefore, the stress intensity factor may be calculated from the stress distribution in the appropriate interval, with a high accuracy.

A Finite Element Solution for Barrel Dynamic Stress

With the APDL language of ANSYS finite element analysis software, the solution program for barrel dynamic stress is developed. The paper describes the pivotal problems of dynamic strength design and provides a foundation for realizing the engineering and programming of barrel dynamic strength design.

Finite-element 3D modeling of stress patterns around a dipping fault

Stresses in a block around a dipping fracture simulating a damage zone of a fault are reconstructed by finite-element modeling. A fracture corresponding to a fault of different lengths, with its plane dipping at different angles, is assumed to follow a lithological interface and to experience either compression or shear. The stress associated with the destruction shows an asymmetrical pattern with different distances from the highest stress sites to the fault plane in the hanging and foot walls. As the dip angle decreases,the high-stress zone becomes wider in the hanging wall but its width changes negligibly in the foot wall.The length of the simulated fault and the deformation type affect only the magnitude of maximum stress,which remains asymmetrical relative to the fault plane. The Lh/Lfratio, where Lhand Lfare the widths of high-stress zones in the hanging and foot walls of the fault, respectively, is inversely proportional to the fault plane dip. The arithmetic mean of this ratio over different fault lengths in fractures subject to compression changes from 0.29 at a dip of 80°to 1.67 at 30°. In the case of shift displacement, ratios are increasing to 1.2 and 2.94, respectively.Usually they consider vertical fault planes and symmetry in a damage zone of faults. Following that assumption may cause errors in reconstructions of stress and fault patterns in areas of complex structural setting. According geological data, we know the structures are different and asymmetric in hanging and foot walls of fault. Thus, it is important to quantify zones of that asymmetry. The modeling results have to be taken into account in studies of natural faults, especially for practical applications in seismic risk mapping, engineering geology, hydrogeology, and tectonics.

Finite Element Analysis of Thermal Stresses in Ceramic/Metal Gradient Thermal Barrier Coatings

This paper studied the thermal stresses of ceramicl metal gradient thermal barrier coating which combines the conceptions of ceramic thermal barrier coating （TBC） and functionally gradient material （FGM）. Thermal stresses and residual thermal stresses were calculated by an ANSYS finite element analysis software. Negative thermal expansion coefficient method was proposed and element birth and death method was applied to analyze the residual thermal stresses which have non-uniform initial temperature field. The numerical results show a good agreement with the analytical results and the experimental results.

A 3D finite element modeling on the relationship between crustal stress and earthquake activity in Liaoning and its vicinity

Based on the latest result in research on 3D seismic wave velocity structure of crust and uppermost mantle and taking geological setting and fracture zones into consideration, a 3D geological model for the studied region is built up. The boundary constraint and force loading boundary condition for the model are determined according to the characteristics of crustal stress field deduced from earthquake focal mechanism and in-situ stress measurement data. Using linear elastic material model a 3D finite element modeling is conducted to study the characteristics of crustal stress field. A comparison analysis between the simulated stress field and earthquake locations reveals that the moderate and strong earthquakes generally occurred in the zones with high shear stress gradient. Furthermore, the paper notices a few potential earthquake-prone regions.

Experimental and finite element analysis of tibial stress fractures using a rabbit model

AIM: To determine if rabbit models can be used to quantify the mechanical behaviour involved in tibial stress fracture(TSF) development.METHODS: Fresh rabbit tibiae were loaded under compression using a specifically-designed test apparatus. Weights were incrementally added up to a load of 30 kg and the mechanical behaviour of the tibia was analysed using tests for buckling, bone strain and hysteresis. Structural mechanics equations were subsequently employed to verify that the results were within the range of values predicted by theory. A finite element(FE) model was developed using cross-sectional computer tomography(CT) images scanned from one of the rabbit bones, and a static load of 6 kg(1.5 times the rabbit's body weight) was applied to represent running. The model was validated using the experimental strain gauge data, then geometric and elemental convergence tests were performed in order to find the minimum number of cross-sectional scans and elements respectively required for convergence. The analysis was then performed using both the model and the experimental results to investigate the mechanical behaviour of the rabbit tibia under compressive load and to examine crack initiation.RESULTS: The experimental tests showed that un der a compressive load of up to 12 kg, the rabbit tibia demonstrates linear behaviour with little hysteresis Up to 30 kg, the bone does not fail by elastic buckling however, there are low levels of tensile stress which predominately occur at and adjacent to the anterio border of the tibial midshaft: this suggests that fatigue failure occurs in these regions, since bone under cycli loading initially fails in tension. The FE model predic tions were consistent with both mechanics theory and the strain gauge results. The model was highly sensi tive to small changes in the position of the applied load due to the high slenderness ratio of the rabbit s tibia. The modelling technique used in the curren study could have applications in the development o human FE models of bone, where, unlike rabbit tibia the model would be relatively insensitive to very sma changes in load position. However, the rabbit mode itself is less beneficial as a tool to understand the me chanical behaviour of TSFs in humans due to the sma size of the rabbit bone and the limitations of human scale CT scanning equipment.CONCLUSION: The current modelling technique could be used to develop human FE models. However, the rabbit model itself has significant limitations in under standing human TSF mechanics.

Three-dimensional analysis of elastic stress distribution of indented ceramic surface by finite element method

The three-dimensional stress distributions in the area surrounding indentation pattern for three different materials, Al2O3, Si3N4 and SiC were analyzed by finite element method(FEM). Those theoretical results were also compared with the experimental ones by Rockwell hardness test. The effect of loading stress on the plastic deformation in specimens, surface was investigated on the assumption of shear strain energy theory by Huber-Mises when the materials were indented. The distributions of nomal stress, shear stress, and Mises stress were analysed with variations of loading conditions. It is clear that the analytical results for the stress distributions, the crack length and its density of probability are in good agreement with the experimental results.

Study on the Stress of DLC/MCT Interface by Finite Element Method

Micro-indention and finite element method (FEM) are used to study the stress at the interface between diamond-like carbon (DLC) film and mercury cadmium telluride (MCT) substrate, with different coating thickness, deposition temperature and indention load. The FEM simulation results show that when Young's modulus ratio of the coating to the substrate Ec/Es<1, Whether a load was applied or not, the interfacial maximum shear stress decreased with the increase of coating thickness. The Von mises stress always concentrated at the interface. The maximum value of the stress locates at the edge of the interface for thin film (h1/h2<0. l), however, it will locate at the center of the interface while the film become thick (h1/h2>0. 1 ). The stress also increased with raising the film deposition temperature, and the temperature affected the strain obviously. When a load was applied, the stress would concentrate where the load was applied, and the stress value is much larger than that of unloading. When the film stress exceeds the film fracture strength, film cracking occurs at the location where load is applied.

INCREMENTAL ANALYSIS FOR NONLINEAR RUBBER-LIKE MATERIALS BY HYBRID STRESS FINITE ELEMENT

In this paper, on the basis of the incremental Reissner variational principle.a nonlinear finite element analysis has been accomplished and a formulation of hybrid stress element has been presented for incompressible Mooney rubber-like materials. The corrected terms of the non-equilibrium force and the incompressibility deviation are considered in the formulation. The computed values of numerical example agree very closely with the exact solution.