A quadrilateral hybrid stress element for Mindlin plates based on incompatible displacements

An hybrid stress element formulation based on internal, incompatible displacements is used to develop efficient Mindlin plate elements. The 4-node quadrilateral Mindlin plate element is derived from a modified energy functional. Both displacements and stresses are defined in the natural co-ordinate interpolation system. The assumed stress field is obtained by tensor transformation and so chosen as to ensure that the element is co-ordinate invariant and stable. Shear locking is avoided through an appropriate identification of the internal, incompatible displacement field. The role played by incompatible displacements in the formulation of hybrid stress elements for thin and moderately thick plates is discussed. Numerical applications are presented to illustrate the accuracy and reliability of the suggested Mindlin plate element.     

A computationally efficient hybrid leakage model for positive displacement compressors and expanders

An empirical frictional correction factor to the isentropic nozzle model has been developed for application to refrigerant leakage modeling in scroll, rotary and other similar compressors and expanders. This correction factor is derived by calculating the leakage mass flow rate with a compressible, variable area, real gas properties model and referencing the results to an isentropic nozzle model. The ratio of flows is correlated to the Reynolds number, a characteristic length and the leakage gap width. A representative selection of fluids and geometries are employed. For all the correlations, at least 93% of the points are predicted within an absolute error band of 20%.     

An assumed displacement hybrid finite element model for linear fracture mechanics

This paper deals with a procedure to calculate the elastic stress intensity factors for arbitrary-shaped cracks in plane stress and plane strain problems. An assumed displacement hybrid finite element model is employed wherein the unknowns in the final algebraic system of equations are the nodal displacements and the elastic stress intensity factors. Special elements, which contain proper singular displacement and stress fields, are used in a fixed region near the crack tip; and the interelement displacement compatibility is satisfied through the use of a Lagrangean multiplier technique. Numerical examples presented include: central as well as edge cracks in tension plates and a quarter-circular crack in a tension plate. Excellent correlations were obtained with available solutions in all the cases. A discussion on the convergence of the present solution is also included.     

Interaction between crack and arbitrarily shaped hole with stress and displacement boundaries

The interaction between a crack and an arbitrarily shaped hole under stress and displacement boundaries in an infinite plane subjected to a remote uniform load is studied. The Green's functions of a point dislocation for the problems are derived and are then used to analyze the interaction problem. The superposition principle is employed to reduce the original problem to two subsidiary problems. The complex stress functions of each problem are composed of two parts, in which the second parts are always holomorphic. Using analytical continuation in conjunction with rational mapping function, the stress functions are obtained in closed form. The interaction of a hole or an inclusion with a crack is solved using dislocations to model the crack and solving a system of singular integral equations. Stress intensity factors for crack tips and stress concentration factors for inclusion corner are determined and plotted for various cases. The affecting ranges of hole and inclusion are investigated.     

弹塑性本构模型计算冻结壁应力场和位移场

应用冻结壁在卸载状态下冻结壁-周围土体共同作用的力学模型,基于大量的冻土应力-应变关系曲线的试验,采用弹塑性非线性本构模型计算冻结壁应力场和位移场.计算结果表明,由于冻结壁在周围土体共同作用下外载比原始水平应力要低,计算的应力场和位移场和有限元模拟接近地.     

An incompatible element for axisymmetric structure and its modification by hybrid method

This paper introduces three four-node quadrilateral axisymmetric elements. The first one is an incompatible element while the second one is a modification of the first element by an extended Hellinger-Reissner principle. The second element is then simplified by incorporating the conceptual idea of free formulation and thus forms the third element. All of the three elements are found to be invariant, insensitive to nodal point numbering, free of locking for nearly incompressible material, able to pass the patch test and do not exhibit the false shear phenomenon. Numerical examples are given and satisfactory predictions are achieved.     

Rupture nucleation on an interface with a power-law relation between stress and displacement discontinuity

We consider rupture initiation and instability on a displacement-weakening interface. It is assumed to follow a power-law relation between a component of displacement discontinuity (whether tensile opening in mode I or shear slippage in modes II or III) and the reduction from peak strength of a corresponding component of stress (normal or shear stress) on the interface. That is, the stress decrease from peak strength, as the interface discontinuity develops, is assumed to be proportional to displacement-discontinuity to some exponent n > 0. The study is done in the 2D context of plane or anti-plane strain, for an initially coherent interface which is subjected to a locally peaked “loading” stress which increases quasi-statically in time. We seek to establish the instability point, when no further quasi-static solution exists for growth of the ruptured zone along the interface, so that dynamic rupture ensues. We have previously addressed the case of linear displacement-weakening (n = 1), and proven the remarkable result that for an unbounded solid, the length of the displacement-weakening zone along the interface at instability is universal, in the sense of being independent of the detailed spatial distribution of the locally peaked loading stress. Present results show that such universality does not apply when n differs from 1. Also, if n < 2/3, there is no phase of initially quasi-static enlargement of the rupturing zone; instead instability will occur as soon as the maximum value of the loading stress reaches the peak strength. We first employ an energy approach to give a Rayleigh–Ritz approximation for the dependence of quasi-static rupture length and maximum displacement-discontinuity on the loading stress distribution of a quadratic form. Results, depending on curvature of the loading distribution, show that qualitative features of the displacement-discontinuity development are significantly controlled by n, with the transition noted at n = 2/3. Predictions of the simple energy approach are in reasonable quantitative agreement with full numerical solutions and give qualitative features correctly.     

Crack border stress and displacement equations revisited

It is more or less accepted in fracture mechanics that the elastic stress and displacements very near to the tip of a plane line crack can be approximated with sufficient accuracy, for all geometries and outer boundary loading conditions, by. a one-parameter representation, i.e. strictly in terms of the stress intensity factors K_I and/or K_II. It is shown here that this presumption which appears to be reasonable on face value, quantitatively speaking, is nevertheless unacceptable as a general proposition. The reason lies with the quite arbitrary practice of omitting the second term of the series representation for the stresses, a contribution which is independent of distance from the crack tip. It is not difficult to show by way of specific examples how such omission can lead to error of serious qualitative nature in the prediction of stress and displacement related quantities of interest.     

Elastic-plastic analysis of Saint-Venant torsion problem by a hybrid stress model

An application of the finite element method to inelastic analysis of the Saint-Venant torsion problem, using a triangular element formulated on the basis of the hybrid stress approach, is described. The stress field in the element is defined by a stress function which is assumed to vary linearly within the element. The warping function on the element boundary is also defined by a linear expression. Numerical results indicate that the method gives an accurate stress solution and is appropriate to the elastic-plastic analysis of bars of arbitrary cross-section which may include multiply connected regions. It is further shown that such phenomena as planar orthogonal plastic anisotropy, strain-hardening and unloading of relevant twisted bar can be treated in a unified manner.     

PAN基炭纤维中sp2杂化的C-C原子键距与结构参数之间关系

利用Raman散射及X射线衍射方法，对不同炭化温度下制备的PAN基炭纤维样品进行了测试。根据Raman散射的测试结果，从Fitzer碳键键距出发，给出了PAN基炭纤维中sp^2杂化的C—C原子键距a0随炭化温度的变化规律。由各样品的X射线衍射测试结果，得到了各样品的结构参数（La、Lc、d002）。分析了sp^杂化的C—C原子键距a0随结构参数（La、Lc、d002）变化的原因。结果表明，C—C原子键距a0与石墨化程度有关，且随La、lc的增大及d002的减小C—C原子键距增大。     

Prediction of stress and displacement fields in stress concentration regions by least squares asymptotic analysis of displacement data

This paper demonstrates that highly accurate predictions of the stress fields, including the peak stress of a stress concentration region, can be obtained easily by a least squares asymptotic analysis (LSAA) of even a relatively sparse set of displacement data from points in this zone lying sufficiently far from the boundary to avoid 'edge effects'.     

New displacement hybrid finite element models for solid continua

The proposed finite element model is based on separate assumptions of interior and interelement displacements and on the assumed boundary tractions of each individual element. The associated variational functional for this model is presented. This method has the same merits of the assumed stress method (References 3 and 4) in that a compatible displacement function at the interelement boundary can be easily constructed, while it can easily be used for shells with distributed loads.     

On the dynamic stress and displacement field associated with a crack propagating across the interface between two media

Two half-spaces with different elastic constants are wellled together and subjected to a longitudinal shear strain at infinity so that the whole system is in a state of anti-plane strain. Suddenly the weld breaks and a crack begins to propagate at right angles to the interface into each of the two media simultaneously with a different velocity in each. This paper attempts to calculate the resulting stress and displacement fields.     

An iterative algorithm to build continuous stress and displacement solutions

An iterative algorithm is presented: it builds a continuous stress and displacement solution starting from the solution of a classical displacement finite element analysis. The modified solution satisfies the virtual work principle, and is much better than the starting solution. The algorithm is very easily included in existing programs. A number of examples shows the efficiency of the method.     

Three-dimensional stress and displacement fields near an elliptical crack front

Local stress and deformation fields for an elliptical crack embedded in an infinite elastic body subjected to normal, shear and mixed loads are considered. Particular emphasis is placed on the direction of propagation of points along the crack border. A confocal curvilinear coordinate system related to a fundamental ellipsoid, and a local spherical coordinate system attached to the crack border are adopted. Using asymptotic analysis, this paper obtains the stress and displacement fields in a plane inclined to the 3D crack front. Results show that the present solutions are independent of the curvature of the ellipse, and different from those given by Sih (1991). Based on two different fracture criteria, crack growth analysis shows that a 3D crack would propagate in the direction of the normal plane along the crack front. As a result, the fracture initiation and propagation of a 3D flat crack can be analyzed in the plane normal to the crack front, and the local fields in the normal plane are the linear superposition of the plane strain mode-I, mode-II, and mode-III crack-tip fields.     

Application of displacement and hybrid strees methods to plane notch and crack problems

For calculating stress concentration factors at plane notches and stress intensity factors at plane cracks a system of finite elements is proposed which uses specially developed triangular hybrid stress elements at the notches and cracks and combines them with triangular elements acording to the displacement method. In formulating the stresses at the notches the Fade-away Law formulated by Neuber has been taken into consideration; for the cracks, formulations are used which exactly contain the stress distribution of Irwin's equations. The quick convergence and high degree of accuracy of this approach are demonstrated by way of test examples.     

A hybrid BEM model

The hybrid stress method is very successful for stress concentration problems.^1–7 Especially for problems of fracture mechanics, procedures can be found that work efficiently for two- and three-dimensional problems. The rate of convergence with this method, evidently, is higher than that with conventional FE models. The BEM procedure, too, works more efficiently, but shows some essential disadvantages against the FEM, such as that for the direct method no symmetric positive definite matrix can be found and that there occur numerical problems at corners.^8,9 This happens also when BEM and FEM are even coupled commonly.^10–12. In the following, a hybrid BEM model will be described which combines the advantages of both the FEM and the BEM. It will be shown in this paper that BEM is very successful in formulating finite element functions for the hybrid assumed stress method.     

Alternate hybrid stress finite element models

Alternate hybrid stress finite element models in which the internal equilibrium equations are satisfied on the average only, while the equilibrium equations along the interelement boundaries and the static boundary conditions are adhered to exactly a priori, are developed. The variational principle and the corresponding finite element formulation, which allows the standard direct stiffness method of structural analysis to be used, are discussed. Triangular elements for a moderately thick plate and a doubly-curved shallow thin shell are developed. Kinematic displacement modes, convergence criteria and bounds for the direct flexibility-influence coefficient are examined.