In this paper, a new class of Zienkiewicz-type non-conforming finite element, in n spatial dimensions with n ≥ 2, is proposed. The new finite element is proved to be convergent for the biharmonic equation.

http://www.math.pku.edu.cn/teachers/wangm/nm5599r.pdf

A new class of Zienkiewicz-type non-conforming element in any dimensions

In this paper, a theoretical framework is constructed on how to develop $$C^0$$ -nonconforming elements for the fourth order elliptic problem. By using the bubble functions, a simple practical method is presented to construct one tetrahedral $$C^{0}$$ -nonconforming element and two cuboid $$C^{0}$$ -nonconforming elements for the fourth order elliptic problem in three spacial dimensions. It is also proved that one element is of first order convergence and other two are of second order convergence. From the best knowledge of us, this is the first success in constructing the second-order convergent nonconforming element for the fourth order elliptic problem.

$$C^{0}$$-nonconforming tetrahedral and cuboid elements for the three-dimensional fourth order elliptic problem

In this paper, using the bubble functions, we construct two C 0-nonconforming triangular prism elements for the fourth order elliptic problem in three dimensions. By the abstract convergence theorem in (Chen et al. in Numer. Math. (2012, accepted)), one element is proved to be of first order convergence and the other one is proved to be of second order convergence.

C0-Nonconforming Triangular Prism Elements for the Three-Dimensional Fourth Order Elliptic Problem

An investigation of the effect of variability of strength and orientation on the factor of safety of tetrahedral wedges with two free surfaces is presented. The study was limited to potential sliding along the line of intersection of the two joint planes. An analytical procedure which combines a deterministic analytical method and the Monte Carlo simulation technique was used to perform the study. Variability of orientations of the joint planes was modeled by the Fisher distributions. Shear strength of the joint planes was modeled by the Mohr Coulomb criterion. Variability of shear strength parameters of the joint planes was modeled by the bivariate normal distributions. The effect of variability of orientation was found to be more pronounced than the effect of variability of strength on the factor of safety. Variability of the factor of safety increased with decreasing correlation between the strength parameters, cohesion, c, and internal friction angle, φ. The effect of variability of c was fou...

Factor of safety of tetrahedral wedges: A probabilistic study

An investigation of effect of variability of strength and orientation on stability of tetrahedral wedges with two free surfaces is presented. Study was limited to potential sliding along the line of intersection of the two joint planes. Minimum rock bolt force and minimum static acceleration were considered as output stability parameters in this study. An analytical procedure which combines a deterministic analytical method and Monte-Carlo simulation technique was used to perform this study. Variability of orientations of the joint planes was modeled by the hemispherical normal distribution. Shear strength of the joint planes was modeled by the Mohr Coulomb criterion. Variability of shear strength parameters of the joint planes was modeled by the bivariate normal distributions. Effect of variability of orientation was found to be more pronounced than the effect of variability of strength on both output parameters. Variability of the magnitudes of the output parameters increased with decreasing co...

Minimum rock bolt force and minimum static acceleration in tetrahedral wedge stability: A probabilistic study

Results of an investigation which is aimed at improving search patterns used in subsurface exploration are presented. Expressions are developed for probability of detection of elliptical targets from various continuous line searches such as parallel lines, square, rhombus, rectangle, and parallelogram. It was assumed that the intersection of the target by search lines provides the condition for detection. Probabilities were calculated to study the effect of target size, shape, and its relative orientation with respect to the search pattern on the probability of intersection for each of the aforementioned search patterns. From this study it was possible to find the relative orientations which provide the maximum probability of intersection for different target sizes and shapes with different patterns. These calculated probabilities were also used to select the optimum search pattern to be used when exploring for elliptical shaped targets. The parallelogram shape was found to be the best pattern for detecti...

Shoung Ouyang

Papers

Target detection probabilities for continuous line search

Probabilistic Modeling Of Shear Strength Of Rock Discontinuities Using Direct Shear Test Data