임의 형상의 강체면 탄소성 접촉 해석을 위한 SPH 알고리듬

Application of an improved contact algorithm for penetration analysis in SPH

This paper aims to analyze large deflections of nanomembranes including surface effects with arbitrary shapes. The nonlinear differential equations of nanomembranes are formulated by using the nonlinear kinematic relations and the surface elasticity theory of Gurtin–Murdoch. The principle of virtual work is applied to establish the three governing partial differential equations of nanomembranes. The coupled boundary element-radial basis functions (BE-RBFs) method is developed to solve the complicated nonlinear problem of nanomembranes. The proposed methodology is based on the analog equation method in conjunction with radial basis functions in order that the boundary line integrals and boundary elements are only involved. The validation and accuracy of the present method are evaluated by comparing the obtained results with those available from other numerical solutions. The proposed formulation can provide the numerical results that correspond to the experimental findings of the monolayer circular graphene membrane by specifying the proper surface properties. The influences of the surface elastic constants and residual surface stress on large deflection responses of nanomembranes are evidently investigated. Moreover, some numerical results of the present formulations could serve as a benchmark for the numerical evaluation of future research. Finally, the interesting results of large deflection analysis of the various nanomembrane shapes using the coupled BE-RBFs method are highlighted.

Body-oriented coordinates applied to the finite-element method

In this paper we show why the postulation scheme based on forces and couples is detrimental when designing novel metamaterials. Instead, the most effective postulation scheme for mechanics is that based on the Principle of Virtual Work formulated by, for example, d'Alembert, Lagrange, Piola, and Paul Germain. In fact, generalized continuum mechanics can be formulated in a coherent way only by basing its foundations on the Principle of Virtual Work while the problem of synthesis of novel metamaterials can be efficiently confronted only when introducing generalized continua as their model at macroscopic level. Once work functionals are postulated, the set of involved generalized forces are identified using the representation theorem for distributions by Laurent Schwartz, forces in particular being zeroth order distributions. Actually, only when limiting the class of considered internal work functionals to first order distributions is the Principle of Virtual Work equivalent to the balances of forces and couples. The predominant Role of the Principle of Virtual Work has been denied by those inductivist scholars who claim that balance laws can be induced by experimentation. The Principle of Virtual Work postulation more truly fits in a falsificationist approach to epistemology.

24 - Systems of Orthogonal Coordinates

A finite element procedure is presented for the analysis of rubber-like hyperelastic materials. The volumetric incompressibility condition of rubber deformation is included in the formulation using the penalty method, while the principle of virtual work is used to derive a nonlinear finite element equation for the large displacement problem that is presented in a total-Lagrangian description. The behavior of rubber deformation is represented by hyperelastic constitutive relations based on a generalized Mooney-Rivlin model. The proposed finite element procedure using analytic differentiation exhibited results that matched very well with those from the well-known commercial packages NISA II and ABAQUS. Furthermore, the convergence of equilibrium iteration is quite slow or frequently fails in the case of near-incompressible rubber. To prevent such phenomenon even for the case that Poisson's ratio is very close to 0.5, Poisson's ratio of 0.49000 is used, first, to get an approximate solution without any difficulty; then the applied load is maintained and Poisson's ratio is increased to 0.49999 following a proposed pattern and adopting a technique of relaxation by monitoring the convergence rate. For a given Poisson ratio near 0.5, with this approach, we could reduce the number of substeps considerably.

Kinematics and dynamics of a 4-PRUR Schönflies parallel manipulator by means of screw theory and the principle of virtual work

A model for predicting sand erosion in 90 degree elbows and bends has been developed based on computational fluid dynamics (CFD), particle tracking and erosion data. After the flow field was obtained from the flow (CFD) model, particles were introduced into the flow and particle trajectories were computed using a Lagrangian approach. A model was also implemented that accounts for the interaction between the particles and the target material. Based on predicted particle impingement velocities, erosion rates and penetration rates were predicted using the empirical equations for erosion ratio. The predicted penetration rates are compared with available experimental data for several different elbows. The agreement between the predicted penetration rates and the experimental data is good. The erosion model is applied to standard (short-radius) elbows and long-radius elbows to understand why long radius elbows have lower erosion (penetration) rates. In addition, based on many predictions and erosion rate results, a new CFD based correlation is developed and is recommended as a first-order approximation for engineering calculations to account for effects of elbow radius on erosion in long-radius elbows. This equation is for computing the ratio of the wall thickness loss (or the penetration rate) in a long-radius elbow to the penetration rate of a standard (short-radius) elbow. The results from the correlation agree well with the trend of available data in the literature.

The nonlinear formulation using the principle of virtual work-energy for free vibration of a large-sag extensible catenary riser in two dimensions is presented in this paper. A support at one end is hinged and the other is a free-sliding roller in the horizontal direction. The catenary riser has a large-sag configuration in the static equilibrium state and is assumed to displace with large amplitude to the motion state. The total virtual work of the catenary riser system involves the virtual strain energy due to bending, the virtual strain energy due to axial deformation, the virtual work done by the effective weight, and the inertia forces. The nonlinear equations of motion for two-dimensional free vibration in the Cartesian coordinate system is developed based on the difference between the Euler's equations in the static state and the displaced state. The linear and nonlinear stiffness matrices of the catenary riser are obtained and the eigenvalue problem is solved using the Galerkin finite element procedure. The natural frequencies and mode shapes are obtained. The results are validated with regard to the reference research addressing the accuracy and efficiency of the proposed nonlinear formulation. The numerical results for free vibration and the effect of the nonlinear behavior for catenary riser are presented.

Comparison of several nonlinear analytical solutions available in the technical literature, and other solutions newly presented here, for relative orbital motion is the subject of this paper. Five core solutions are emphasized: the Quadratic Volterra solution using rectangular coordinates, the Multiple Scales solution using spherical coordinates, the Absolute Difference solution using orbital element difference coordinates, the Double Transformation solution using cylindrical coordinates, and the Double Transformation solution using spherical coordinates. Two additional solutions denoted the Approximated Double Transformation solutions using either cylindrical or spherical coordinates are also considered. Each solution is unique in its assumptions, formulation, and derivation, but all are approximate analytical based solutions with the objective of providing applicational utility with increased fidelity. Analysis is restricted to Keplerian motion with a circular reference orbit. Five of the solutions utilize series expansion concepts to second order accuracy, while the remaining two solutions utilize first order core accuracy coupled with nonlinear transformations. All results are transformed to relative rectangular coordinates so that various solutions are directly comparable. The intent of the study is to expose and discuss any significant similarities and/or differences in the various model solutions.

To describe the configuration of a multi-body system, Cartesian coordinate systems are attached to all bodies comprising the system. Their connections through joints and force elements are efficiently expressed by using 4×4 matrices of the homogeneous transformation, presented by Denavit and Hartenberg in 1955. However, at this time, there is no systematic method to compute velocities and angular velocities using the matrices of such homogeneous transformations. In this paper, homogeneous transformation matrices are identified as a subset of a Lie group, called the special Euclidean group denoted by SE(3). This observation enables the usage of the Lie group theory in multibody kinematics. The effective use of the theory is built upon a platform of a moving frame method as presented in this paper. In this method, for each body-attached Cartesian coordinate system, the coordinate vector basis is written explicitly following Élie Cartan. This moving frame notation enables us to use the Lie algebra of SE(3), denoted by se(3), to compute velocities and angular velocities by minimizing the complexities of the Lie group theory. For kinetics, a variational method is established in se(3) by deriving a relationship between a virtual angular velocities and the corresponding virtual rotational displacements. This constrained variation of virtual angular velocities allows the derivation of the d’Alembert principle of virtual work from Hamilton’s principle for multibody systems. Utilizing this variational tool, we present a systematic computation of equations of motion from Hamilton’s principle. Finally, we reduce the spatial dynamics to planar dynamics and list the simplifications achieved in the two-dimensional problems using SE(2). Then, for a two-degree-of-freedom manipulator the analytical equations of motion are obtained to demonstrate the power of the moving frame method.

One of the key aspects of a successful drilling is effective optimization of ROP (Rate of Penetration). Because of the complexity and heterogeneity of formation permeability, the traditional ROP analysis method are limited by drilling prediction. With the accumulation of geological data and drilling records, new methods such as artificial neural network and particle swarm optimization have become powerful tools for obtaining optimization parameters. A ROP optimization method based on deep learning neural network and particle swarm optimization is proposed. Firstly, the prediction model of target wells is established from well logging data by using deep learning neural network. Secondly, the optimized wellbore operation parameters are obtained by using PSO algorithm. At last, the RNN learning algorithm is updated by introducing recovery factor. And also, for the sake of the realization of constraints, a penalty function is introduced. After analyzed logging data of a group of wells in Shunbei area, the experimental results showed that this method can effectively use engineering data to predict drilling rate and optimize drilling parameters.

Chapter 4 - Virtual work and energy methods

A derivation for the finite element equations of consolidation by the principle of virtual work and virtual complementary work is presented. This provides a simple alternative to derivation by variational principles or the Laplace transform. In the final part of the paper the equations are rearranged into a form suitable for time stepping for non‐linear applications.

The principle of virtual work is the starting point for the formulation of the finite element method for solids and structures and we dedicate this chapter to its study.We start by introducing the principle of virtual work for a 1-D model and by exploring the fundamental facts. Then, the principle is given for the 3-D elasticity model and for the remaining mathematical models discussed in Chapter 4.In the last section, we introduce some energy concepts in 3-D analysis which provide alternative ways to formulate the mathematical models of Chapters 3 and 4. These energy based formulations will be useful in Chapters 6 and 8.KeywordsVirtual WorkElasticity ProblemTotal Potential EnergyVirtual DisplacementDisplacement Boundary ConditionThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.