Generalized mixed finite element method for 3D elasticity problems

Without applying any stable element techniques in the mixed methods, two simple generalized mixed element(GME) formulations were derived by combining the minimum potential energy principle and Hellinger–Reissner(H–R) variational principle. The main features of the GME formulations are that the common C0-continuous polynomial shape functions for displacement methods are used to express both displacement and stress variables, and the coefficient matrix of these formulations is not only automatically symmetric but also invertible. Hence, the numerical results of the generalized mixed methods based on the GME formulations are stable. Displacement as well as stress results can be obtained directly from the algebraic system for finite element analysis after introducing stress and displacement boundary conditions simultaneously. Numerical examples show that displacement and stress results retain the same accuracy. The results of the noncompatible generalized mixed method proposed herein are more accurate than those of the standard noncompatible displacement method. The noncompatible generalized mixed element is less sensitive to element geometric distortions.

A NEW HIGH-ORDER MULTI-JOINT FINITE ELEMENTFOR THIN-WALLED BAR

A new high-order multi-joint finite element for thin-walled bar was derived from the Hermite interpolation polynomial and minimum potential energy principle. This element's characteristics are that it is of high accuracy and can be used in finite method analysis of bridge, tall mega-structure building.

Post-Buckling Analysis for Elastic Thin Plate Under Unilateral Frictionless Restraint

To investigate the buckling and post buckling behaviors of elastic thin plate under frictionless unilateral restraint, enduring the coupling action of lognitudinal and transverse loads, the principle of minimum potential energy and variational method are used and series functions with unknown coefficients are taken as trial functions of functional to solve the large deflection and non linear bending problem of a thin plate and find relation curves between deflection of plate and loads. The proposed method can capture the buckling and post buckling behaviors of a thin plate in different geometrical and load boundary conditions. The analysis confirms that there occur snap and bifurcation behaviors in the post buckling stage of the plate. And these results show the validity of the variational method for solving buckling problems of thin plate.

A nonlinear rheological model of backfill material for retaining roadways and the analysis of its stability

The long-term stability of backfill material is the key to retaining roadways successfully. In order to study the rheological deformation of backfill material and its long-term stability, given the visco-elastoplastic properties of this material, we introduced a softening and a hardening function for a new nonlinear the- ological model with time-varying parameters. Based on this, we presented the instability condition of this model by using the principle of minimum potential energy. Combined with engineering practice, we cal- culated the urlstable time period of backfill material. The results show that the time of instability of the backfill material relate to the initial parameters of the material, ＂the coefficients decided by temperature and the ratio of the plastic zone of the backfill material. Based on the results of our analysis from the point of view of energy, we can quickly obtain the time of instability of this model from our graphical analysis. The time of instability of the backfill material obtained from our investigation coincides with an actual project.

HOMOTOPY CONTINUATION ALGORITHM FOR STRUCTURAL DAMAGE IDENTIFICATION

A new method is put forward for structural damage identification based on the homotopy continuation algorithm. A numerical example is presented to verify the method. The beams with different damage locations and different damage extents are identified by this method. The numerical examples have proved that this new method is capable of easy convergence, which is not sensitive to the initial iterative values. It is effective for accurately identifying multiple damages. By incorporating the finite element method into the homotopy continuation algorithm, the damage identifying ability of the new method can be greatly enhanced.

Generalized stress field in granular soils heap with RayleigheRitz method

The stress field in granular soils heap(including piled coal) will have a non-negligible impact on the settlement of the underlying soils. It is usually obtained by measurements and numerical simulations.Because the former method is not reliable as pressure cells instrumented on the interface between piled coal and the underlying soft soil do not work well, results from numerical methods alone are necessary to be doubly checked with one more method before they are extended to more complex cases. The generalized stress field in granular soils heap is analyzed with Rayleighe Ritz method. The problem is divided into two cases: case A without horizontal constraint on the base and case B with horizontal constraint on the base. In both cases, the displacement functions u(x, y) and v(x, y) are assumed to be cubic polynomials with 12 undetermined parameters, which will satisfy the Cauchy’s partial differential equations, generalized Hooke’s law and boundary equations. A function is built with the Rayleighe Ritz method according to the principle of minimum potential energy, and the problem is converted into solving two undetermined parameters through the variation of the function, while the other parameters are expressed in terms of these two parameters. By comparison of results from the Rayleighe Ritz method and numerical simulations, it is demonstrated that the Rayleighe Ritz method is feasible to study the generalized stress field in granular soils heap. Solutions from numerical methods are verified before being extended to more complicated cases.

A theoretical model of rigid projectile perforation of concrete slabs using the energy method

Projectile perforation of concrete slabs will produce numerous concrete fragments on the rear face of the concrete slabs. These concrete fragments will cause serious secondary damage to the indoor personnel and equipment of protective structures.Accurately evaluating the damage area of concrete slabs is an important problem. Therefore, a theoretical model of a rigid projectile perforation of concrete slabs is constructed using the energy method in this paper. In this model, a new shear failure method is proposed to calculate the energy consumption of the shear formation by combining with the von-Mises failure criterion and failure strain. Based on the energy conservation and principle of minimum potential energy, explicit equations for the perforation performance are formulated. The theoretical predictions agree well with the experimental results. Furthermore,experiments on a high-speed projectile normal perforation of concrete are carried out to verify the accuracy of the corresponding theoretical prediction.