Meshless Local Petrov-Galerkin Method for Bending Problems


Book Description

Recent literature shows extensive research work on meshless or element-free methods as alternatives to the versatile Finite Element Method. One such meshless method is the Meshless Local Petrov-Galerkin (MLPG) method. In this report, the method is developed for bending of beams - C1 problems. A generalized moving least squares (GMLS) interpolation is used to construct the trial functions, and spline and power weight functions are used as the test functions. The method is applied to problems for which exact solutions are available to evaluate its effectiveness. The accuracy of the method is demonstrated for problems with load discontinuities and continuous beam problems. A Petrov-Galerkin implementation of the method is shown to greatly reduce computational time and effort and is thus preferable over the previously developed Galerkin approach. The MLPG method for beam problems yields very accurate deflections and slopes and continuous moment and shear forces without the need for elaborate post-processing techniques. Phillips, Dawn R. and Raju, Ivatury S. Langley Research Center RTOP 706-21-21-06




Methods of Fundamental Solutions in Solid Mechanics


Book Description

Methods of Fundamental Solutions in Solid Mechanics presents the fundamentals of continuum mechanics, the foundational concepts of the MFS, and methodologies and applications to various engineering problems. Eight chapters give an overview of meshless methods, the mechanics of solids and structures, the basics of fundamental solutions and radical basis functions, meshless analysis for thin beam bending, thin plate bending, two-dimensional elastic, plane piezoelectric problems, and heat transfer in heterogeneous media. The book presents a working knowledge of the MFS that is aimed at solving real-world engineering problems through an understanding of the physical and mathematical characteristics of the MFS and its applications. - Explains foundational concepts for the method of fundamental solutions (MFS) for the advanced numerical analysis of solid mechanics and heat transfer - Extends the application of the MFS for use with complex problems - Considers the majority of engineering problems, including beam bending, plate bending, elasticity, piezoelectricity and heat transfer - Gives detailed solution procedures for engineering problems - Offers a practical guide, complete with engineering examples, for the application of the MFS to real-world physical and engineering challenges







High-Performance Computing Systems and Technologies in Scientific Research, Automation of Control and Production


Book Description

This book constitutes selected revised and extended papers from the 10th International Conference on High-Performance Computing Systems and Technologies in Scientific Research, Automation of Control and Production, HPCST 2020, Barnaul, Russia, in May 2020. Due to the COVID-19 pancemic the conference was partly held in virtual mode. The 14 full papers presented in this volume were thoroughly reviewed and selected form 51 submissions. The papers are organized in topical sections on hardware for high-performance computing and its applications; information technologies and computer simulation of physical phenomena.




Advances in Multiphysics Simulation and Experimental Testing of MEMS


Book Description

This volume takes a much needed multiphysical approach to the numerical and experimental evaluation of the mechanical properties of MEMS and NEMS. The contributed chapters present many of the most recent developments in fields ranging from microfluids and damping to structural analysis, topology optimization and nanoscale simulations. The book responds to a growing need emerging in academia and industry to merge different areas of expertise towards a unified design and analysis of MEMS and NEMS.




Particle Methods for Multi-Scale and Multi-physics


Book Description

Multi-scale and multi-physics modeling is useful and important for all areas in engineering and sciences. Particle Methods for Multi-Scale and Multi-Physics systematically addresses some major particle methods for modeling multi-scale and multi-physical problems in engineering and sciences. It contains different particle methods from atomistic scales to continuum scales, with emphasis on molecular dynamics (MD), dissipative particle dynamics (DPD) and smoothed particle hydrodynamics (SPH). This book covers the theoretical background, numerical techniques and many interesting applications of the particle methods discussed in this text, especially in: micro-fluidics and bio-fluidics (e.g., micro drop dynamics, movement and suspension of macro-molecules, cell deformation and migration); environmental and geophysical flows (e.g., saturated and unsaturated flows in porous media and fractures); and free surface flows with possible interacting solid objects (e.g., wave impact, liquid sloshing, water entry and exit, oil spill and boom movement). The presented methodologies, techniques and example applications will benefit students, researchers and professionals in computational engineering and sciences --




Computer Vision/Computer Graphics Collaboration Techniques


Book Description

This book constitutes the refereed proceedings of the 4th International Conference on Computer Vision/Computer Graphics Collaboration Techniques, MIRAGE 2009, held in Rocquencourt, France, in May 2009. The 41 revised full papers presented were carefully reviewed and selected from a total of 83 submissions. The papers cover a wide range of topics with focus on Computer Vision/Computer Graphics collaboration techniques involving image analysis/synthesis approaches especially concerning theoretical, computational, experimental or industrial aspects of model-based image analysis and image-based model synthesis.




Meshfree Particle Methods


Book Description

Meshfree Particle Methods is a comprehensive and systematic exposition of particle methods, meshfree Galerkin and partitition of unity methods, molecular dynamics methods, and multiscale methods. Most theories, computational formulations, and simulation results presented are recent developments in meshfree methods. They were either just published recently or even have not been published yet, many of them resulting from the authors ́ own research. The presentation of the technical content is heuristic and explanatory with a balance between mathematical rigor and engineering practice. It can be used as a graduate textbook or a comprehensive source for researchers, providing the state of the art on Meshfree Particle Methods.




Analytical or Semi-analytical Solutions of Functionally Graded Material Structures


Book Description

This book provides a comprehensive introduction to the analysis of functionally graded materials and structures. Functionally graded materials (FGMs), in which the volume fractions of two or more constituent materials are designed to vary continuously as a function of position along certain direction(s), have been developed and studied over the past three decades. The major advantage of FGMs is that no distinct internal boundaries exist, and failures from interfacial stress concentrations developed in conventional components can be avoided. The gradual change of material properties can be tailored to different applications and working environments. As these materials’ range of application expands, new methodologies have to be developed to characterize them, and to design and analyze structural components made of them. Despite a number of existing papers on the analysis of functionally graded materials and structures, there is no single book that is devoted entirely to the analysis of functionally graded beams, plates and shells using different methods, e.g.,analytical or semi-analytical methods. Filling this gap in the literature, the book offers a valuable reference resource for senior undergraduates, graduate students, researchers, and engineers in this field. The results presented here can be used as a benchmark for checking the validity and accuracy of other numerical solutions. They can also be used directly in the design of functionally graded materials and structures.