Cmes-computer Modeling in Engineering & Sciences 

About: Cmes-computer Modeling in Engineering & Sciences is an academic journal published by Tech Science Press. The journal publishes majorly in the area(s): Computer science & Finite element method. It has an ISSN identifier of 1526-1492. It is also open access. Over the lifetime, 2813 publications have been published receiving 32250 citations. The journal is also known as: Computer modeling in engineering and sciences & CMES.

The Generalized Interpolation Material Point Method

Abstract: The Material Point Method (MPM) discrete solution procedure for computational solid mechanics is generalized using a variational form and a Petrov- Galerkin discretization scheme, resulting in a family of methods named the Generalized Interpolation Material Point (GIMP) methods. The generalization permits iden- tification with aspects of other point or node based dis- crete solution techniques which do not use a body-fixed grid, i.e. the "meshless methods". Similarities are noted and some practical advantages relative to some of these methods are identified. Examples are used to demon- strate and explain numerical artifact noise which can be expected in MPM calculations. This noise results in non- physical local variations at the material points, where constitutive response is evaluated. It is shown to destroy the explicit solution in one case, and seriously degrade it in another. History dependent, inelastic constitutive laws can be expected to evolve erroneously and report inac- curate stress states because of noisy input. The noise is due to the lack of smoothness of the interpolation func- tions, and occurs due to material points crossing compu- tational grid boundaries. The next degree of smoothness available in the GIMP methods is shown to be capable of eliminating cell crossing noise. keyword: MPM, PIC, meshless methods, Petrov- Galerkin discretization.

The Meshless Local Petrov-Galerkin (MLPG) Method: A Simple \& Less-costly Alternative to the Finite Element and Boundary Element Methods

Abstract: A comparison study of the efficiency and ac- curacy of a variety of meshless trial and test functions is presented in this paper, based on the general concept of the meshless local Petrov-Galerkin (MLPG) method. 5 types of trial functions, and 6 types of test functions are explored. Different test functions result in different MLPG methods, and six such MLPG methods are pre- sented in this paper. In all these six MLPG methods, absolutely no meshes are needed either for the interpo- lation of the trial and test functions, or for the integration of the weak-form; while other meshless methods require background cells. Because complicated shape functions for the trial function are inevitable at the present stage, in order to develop a fast and robust meshless method, we explore ways to avoid the use of a domain integral in the weak-form, by choosing an appropriate test function. The MLPG5 method (wherein the local, nodal-based test function, over a local sub-domain Ω s (or Ω te) centered at a node, is the Heaviside step function) avoids the need for both a domain integral in the attendant symmetric weak-form as well as a singular integral. Convergence studies in the numerical examples show that all of the MLPG methods possess excellent rates of convergence, for both the unknown variables and their derivatives. An analysis of computational costs shows that the MLPG5 method is less expensive, both in computational costs as well as definitely in human-labor costs, than the FEM, or BEM. Thus, due to its speed, accuracy and robustness, the MLPG5 method may be expected to replace the FEM, in the near future.

The Meshless Local Petrov-Galerkin (MLPG) Method for Solving Incompressible Navier-Stokes Equations

Abstract: The truly Meshless Local Petrov-Galerkin (MLPG) method is extended to solve the incompressible Navier-Stokes equations. The local weak form is modi- fied in a very careful way so as to ovecome the so-called Babuska-Brezzi conditions. In addition, The upwinding scheme as developed in Lin and Atluri (2000a) and Lin and Atluri (2000b) is used to stabilize the convection operator in the streamline direction. Numerical results for benchmark problems show that the MLPG method is very promising to solve the convection dominated fluid mechanics problems. keyword: MLPG, MLS, Babuconditions, upwinding scheme, incompressible flow, Navier-Stokes equations.

An Improved Contact Algorithm for the Material Point Method and Application to Stress Propagation in Granular Material

Abstract: Contact between deformable bodies is a dif- cult problem in the analysis of engineering systems A new approach to contact has been implemented us- ing the Material Point Method for solid mechanics, Bar- denhagen, Brackbill, and Sulsky (2000a) Here two im- provements to the algorithm are described The rst is to include the normal traction in the contact logic to more appropriately determine the free separation crite- rion The second is to provide numerical stability by scaling the contact impulse when computational grid in- formation is suspect, a condition which can be expected to occur occasionally as material bodies move through the computational grid The modications described preserve important properties of the original algorithm, namely conservation of momentum, and the use of global quantities which obviate the need for neighbor searches and result in the computational cost scaling linearly with the number of contacting bodies The algorithm is demonstrated on several examples Deformable body so- lutions compare favorably with several problems which, for rigid bodies, have analytical solutions A much more demanding simulation of stress propagation through ide- alized granular material, for which high delity data has been obtained, is examined in detail Excellent quali- tative agreement is found for a variety of contact con- ditions Important material parameters needed for more quantitative comparisons are identied