By G.R. Liu
This ebook goals to offer meshfree equipment in a pleasant and simple demeanour, in order that rookies can conveniently comprehend, understand, application, enforce, practice and expand those tools. It offers first the basics of numerical research which are rather vital to meshfree equipment. regular meshfree equipment, resembling EFG, RPIM, MLPG, LRPIM, MWS and collocation equipment are then brought systematically detailing the formula, numerical implementation and programming. Many well-tested computing device resource codes constructed through the authors are connected with beneficial descriptions. the appliance of the codes may be easily played utilizing the examples with enter and output records given in desk shape. those codes encompass lots of the simple meshfree options, and will be simply prolonged to different diversifications of extra advanced strategies of meshfree tools. Readers can simply perform with the codes supplied to powerful study and understand the fundamentals of meshfree equipment.
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Extra resources for An Introduction to Meshfree Methods and Their Programming
Convergence of the results of the axial displacements obtained using different weighted residual methods with different terms in the approximate solution. 1) Approximate the field function (displacement) in terms of the nodal variables using the trial or shape functions; let d be the vector consisting of all the nodal displacements in the problem domain. 2) Express the total potential energy, 3, in terms of the nodal variables d. 101) where 3s is the strain energy, and the Wf is the work done by the external forces.
This book will use weak-form formulations to form discretized system equations of MFree weak-form methods† for mechanics problems of solids † A detailed discussion of the categories for mesh-free methods will be discussed in Chapter 2. 14 Chapter 1 and fluids (see Chapters 4 and 5). The strong-form formulation based on the collocation approach will also be used to formulate the so-called MFree strong-form methods (or MFree collocation method, see Chapter 6). In addition, both of them will be combined to formulate the MFree weak-strong (MWS) form method (see Chapter 7), where the local weak-form is utilized on and near the natural boundary to obtain stabilized solution.
It has been and will still be used for developing new MFree methods. All these approaches will be adapted in this book for creating discretized system equations for various types of MFree methods. 4 WEIGHTED RESIDUAL METHOD The weighted residual method is a general and extremely powerful method for obtaining approximate solutions for ordinary differential equations (ODEs) or partial differential equations (PDEs). Many numerical methods can be based on the general weighted residual method. Hence, this section discusses some of those numerical methods using a simple example problem.