Optimal structural topologies with transmissible loads

In optimal topological design of structures one obtains the configuration of optimal structures when the design domain, the displacement boundary conditions and the applied loads are specified. In the optimal structure one often notices a marked difference between the main bearing structure and the load transfer zones. The latter are composed of relatively light elements the exact nature of which is not always very distinct. The main purpose of this paper is to allow the main bearing part of the structure to emerge. Moreover the actual location of the load along its line of action is not always a design requirement. In order to include this relaxed condition regarding the loading position the concept of transmissible or sliding forces is introduced in topological design of structures. A transmissible force is a force of given magnitude and direction which can be applied at any point along the line of action of the force. The optimization formulation is similar to standard topological design procedure in addition to the condition of transmissability of the forces. It is shown that this condition reduces to an equal displacement constraint along the line of action of the forces. The method is illustrated by typical structural examples. It is observed that this numerical method produces indeed crisp images of the main structural components, unblurred by the secondary load transfer elements. It is also indicated that many results are often replicas of Prager structures which were previously obtained by analytical methods. Received March 3, 1999     

弹塑性土质边坡再生核质点法分析

针对土质边坡的稳定性问题，提出了利用无网格法中的再生核质点法（RKPM）进行弹塑性分析的方法.在介绍RKPM基本理论的基础上，探讨了其近似函数的建立与有限元法的区别，并用Galerkin法对控制方法进行了离散.针对边坡稳定的平面应变问题，假设工程土性质符合Drucker Prager本构关系，基于相关联流动法则，采用强度折减系数法得到了土质边坡在自重作用下的安全系数和失稳变形形式.结果表明，采用该分析方法能克服数值计算中网格畸变，得到的安全系数与极限平衡法结果接近，并能直观反映边坡失稳时的变形状态和形式.     

塑性应变准则在油井出砂预测中的应用

用塑性应变准则建立了油井出砂预测的有限元力学模型，岩石的屈服应力准则用Drucker-Prager准则。在某油画地层参数下，用该模型得到了不同井筒压差所对应井壁附近的塑性应力、应变变化结果，用这些结果可预测油井出砂情况。根据临界塑性应变，确定了井壁不出砂的临界生产压差，为油井正常生产提供了理论数据。     

Some micromechanical models of elastoplastic behaviors of porous geomaterials

Some micromechanics-based constitutive models are presented in this study for porous geomaterials. These micro-macro mechanical models focus on the effect of porosity and the inclusions on the macroscopic elastoplastic behaviors of porous materials. In order to consider the effect of pores and the compressibility of the matrix, some macroscopic criteria are presented firstly for ductile porous medium having one population of pores with different types of matrix (von Mises, Green type, Mises–Schleicher and Drucker–Prager). Based on different homogenization techniques, these models are extended to the double porous materials with two populations of pores at different scales and a Drucker–Prager solid phase at the microscale. Based on these macroscopic criteria, complete constitutive models are formulated and implemented to describe the overall responses of typical porous geomaterials (sandstone, porous chalk and argillite). Comparisons between the numerical predictions and experimental data with different confining pressures or different mineralogical composites show the capabilities of these micromechanics-based models, which take into account the effects of microstructure on the macroscopic behavior and significantly improve the phenomenological ones.     

3D mechanical modeling of soil orthogonal cutting under a single reamer cutter based on Drucker–Prager criterion

Reamers have been the major implement used to enlarge the hole size in reaming stage of horizontal directional drilling (HDD). The choice of its available structural design becomes critical to maximize the rate of penetration and minimize the tripping time, thereby decreasing the cost of operations and the risk of experiencing stability problems. Moreover, because the duration period of a HDD project is largely dependent on the reaming stage, it is crucial to study the reaming efficiency by use of the appropriate operating conditions (cutting angle and depth). In the paper, the reaming efficiency of reamer is analyzed based on the development of a 3D analytical cutting force model of soil orthogonal cutting under a single reamer cutter. Focusing on the soil orthogonal cutting mechanism under a single reamer cutter, the interaction and friction between soil and cutter and the shear action of 3D shear zone are comprehensively considered, consequently the mechanical properties are given. Based on these analyses and using the Drucker–Prager criterion given a weight to the intermediate principal stress, the analytical models are proposed. In addition, this paper presents 3D FEM simulations for the analysis of soil orthogonal cutting under a single reamer cutter. The subject has been covered in two parts. Part one deals with the verification of the analytical cutting force model, the other focuses on the assessment and selection of the criterions of shear angle. The analytical cutting force model presented provides the capability to evaluate cutter loading for utilization of a single cutter with different rake angles to cut soils, and to plot the effect of change in the rake angle. Finally, the optimum rake angle of single reamer cutter was obtained. The results of this analysis can be integrated to study reamer performance. It can also provide a guideline to the application and design of the reamer assembly for various soils.     

Resolution of Binary Coding of Real-Valued Vectors by Hyperrectangular Receiptive Fields

Schemes of binary coding of real-valued vectors are considered. Hyperrectangular receptive fields such as RSC and Prager randomly distributed fields and CMAC regular fields are analyzed. Theoretical and experimental estimations of resolving power (resolution) of codes and the comparative analysis of coding schemes are presented. __________ Translated from Kibernetika i Sistemnyi Analiz, No. 5, pp. 3–15, September–October 2005.     

Stability analysis of vertical boreholes using the Mogi–Coulomb failure criterion

A main aspect of wellbore stability analysis is the selection of an appropriate rock failure criterion. The most commonly used criterion for brittle failure of rocks is the Mohr–Coulomb criterion. This criterion involves only the maximum and minimum principal stresses, σ₁ and σ₃, and therefore assumes that the intermediate stress σ₂ has no influence on rock strength. As the Mohr–Coulomb criterion ignores the strengthening effect of the intermediate stress, it is expected to be too conservative in estimating the critical mud weight required to maintain wellbore stability. Recently, Al-Ajmi and Zimmerman [Relationship between the parameters of the Mogi and Coulomb failure criterion. Int J Rock Mech Min Sci 2005;42(3):431–39.] developed the Mogi–Coulomb failure criterion, and showed that it is reasonably accurate in modelling polyaxial failure data from a variety of rocks. We then develop a model for the stability of vertical boreholes, using linear elasticity theory to calculate the stresses, and the fully-polyaxial Mogi–Coulomb criterion to predict failure. Our model leads to easily computed expressions for the critical mud weight required to maintain wellbore stability.     

Kinematic limit analysis modelling by a regularization approach and finite element method

Kinematical approach by limit analysis is one of the fundamental methods used to predict the plastic limit state and it is applied successfully to deal with engineering problems in solid mechanics. The kinematical approach consists of minimizing the plastic dissipation power throughout the body, produced by plasticity, which involves functional with norm integrand. Besides, to derive the stress field within the body, one uses the inverse plastic law that is a subdifferential of the dissipation power. The complexity and possible singularity in the derivatives of functionals become a source of many numerical troubles. To overcome these encountered difficulties, we propose a solving algorithm by using a regularization procedure on the basis of the inf‐convolution operation. Some numerical applications by plane strain or axisymmetric finite element method are presented to illustrate the algorithm. Copyright © 2003 John Wiley & Sons, Ltd.     

Optimal transportation meshfree method in geotechnical engineering problems under large deformation regime

Meshfree methods have been demonstrated as suitable and strong alternatives to the more standard numerical schemes such as finite elements or finite differences. Moreover, when formulated in a Lagrangian approach, they are appropriate for capturing soil behavior under high‐strain levels. In this paper, the optimal transportation meshfree method has been applied for the first time to geotechnical problems undergoing large deformations. All the features employed in the current methodology (ie, F‐bar, explicit viscoplastic integration, and master‐slave contact) are described and validated separately. Finally, the model is applied to the particular case of shallow foundations by using von Mises and Drucker‐Prager yield criteria to find the load at failure in the. The presented methodology is demonstrated to be robust and accurate when solving this type of problems.