Applied principle of minimum potential energy in analyzing buckle phenomenon of cold rolled strip

When solving buckling type based on minimum potential energy, it is first to make hypothesis for strip buckling type. Under the simple strain condition, buckling type and strain distribution have a certain similarity, so the hypothesis is reasonable comparatively. However, under the complicated strain condition, it is difficult to give more reasonable buckling type. Moreover, the existing algorithms usually ignore the effect which the transverse stress and the shear stress have on the buckling type. After assuming strip was only affected by shear stress for the edge wave and affected by both transverse stress and the shear stress for the center wave in the paper, the buckling form of strip under simple strain situation was calculated. It was seen from the calculating result that wave height and half wavelength were smaller than those of the existing algorithms, and the wave height and half wavelength of edge wave were all bigger than those of center wave in the same stress distribution. Secondly, a more reasonable hypothesis method of buckling type for the complicated stress distribution was put forward. After analyzing, the result showed that it was more reasonable by using the optimizing algorithm.

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.

SOLUTION OF GENERALIZED COORDINATE FOR WARPING FOR NATURALLY CURVED AND TWISTED BEAMS

A theoretical method for static analysis of naturally curved and twisted beams under complicated loads was presented, with special attention devoted to the solving process of governing equations which take into account the effects of torsion-related warping as well as transverse shear deformations. These governing equations, in special cases, can be readily solved and yield the solutions to the problem. The solutions can be used for the analysis of the beams, including the calculation of various internal forces, stresses, strains and displacements. The present theory will be used to investigate the stresses and displacements of a plane curved beam subjected to the action of horizontal and vertical distributed loads. The numerical results obtained by the present theory are found to be in very good agreement with the results of the FEM results. Besides, the present theory is not limited to the beams with a double symmetric cross-section, it can also be extended to those with arbitrary cross-sectional shape.

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.

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.

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.

THE DERIVATION OF EXACT STATIC CONDITIONS AT THE CORNER POINTS FOR THE BENDING OF THICK RECTANGULAR PLATES

In this paper, exact static conditions at the corner points for the bending of thickrectangular ptates are strictly. derived from the theorem of minimum potentialenerg[1].