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Extended Finite Element Method
The extended finite element method (XFEM), is a numerical technique based on the generalized finite element method (GFEM) and the partition of unity method (PUM). It extends the classical finite element method (FEM) approach by enriching the solution space for solutions to differential equations with discontinuous functions. History The extended finite element method (XFEM) was developed in 1999 by Ted Belytschko and collaborators, to help alleviate shortcomings of the finite element method and has been used to model the propagation of various discontinuities: strong ( cracks) and weak (material interfaces). The idea behind XFEM is to retain most advantages of meshfree methods while alleviating their negative sides. Rationale The extended finite element method was developed to ease difficulties in solving problems with localized features that are not efficiently resolved by mesh refinement. One of the initial applications was the modelling of fractures in a material. In ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Example Of 2D Mesh
Example may refer to: * '' exempli gratia'' (e.g.), usually read out in English as "for example" * .example, reserved as a domain name that may not be installed as a top-level domain of the Internet ** example.com, example.net, example.org, example.edu, second-level domain names reserved for use in documentation as examples * HMS ''Example'' (P165), an Archer-class patrol and training vessel of the Royal Navy Arts * ''The Example'', a 1634 play by James Shirley * ''The Example'' (comics), a 2009 graphic novel by Tom Taylor and Colin Wilson * Example (musician), the British dance musician Elliot John Gleave (born 1982) * ''Example'' (album), a 1995 album by American rock band For Squirrels See also * * Exemplar (other), a prototype or model which others can use to understand a topic better * Exemplum, medieval collections of short stories to be told in sermons * Eixample The Eixample (; ) is a district of Barcelona between the old city ( Ciutat Vella) an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Radioss
Altair Radioss is a multidisciplinary finite element solver developed by Altair Engineering. It can solve both linear and non-linear problems. It is a finite element solver using implicit and explicit integration schemes for the solution of engineering problems, from linear statics and linear dynamics to nonlinear transient dynamics and mechanical systems. This multidisciplinary solver enables designers to maximize performance related to durability, NVH, crash, safety, manufacturability, and fluid-structure interaction, in order to bring products to market faster. Since the 2021 release, Radioss has supported input in the LS-DYNA input format as well as the Radioss 'Block' Format OpenRadioss, an open source version of Radioss, sharing the capabilities, input and output formats of Altair Radioss, was released on September the 8th 2022. Disciplines * Linear static analysis * Non-linear explicit dynamic analysis * Non-linear implicit quasi-static analysis * Normal modes a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Continuum Mechanics
Continuum mechanics is a branch of mechanics that deals with the mechanical behavior of materials modeled as a continuous mass rather than as discrete particles. The French mathematician Augustin-Louis Cauchy was the first to formulate such models in the 19th century. Explanation A continuum model assumes that the substance of the object fills the space it occupies. Modeling objects in this way ignores the fact that matter is made of atoms, and so is not continuous; however, on length scales much greater than that of inter-atomic distances, such models are highly accurate. These models can be used to derive differential equations that describe the behavior of such objects using physical laws, such as mass conservation, momentum conservation, and energy conservation, and some information about the material is provided by constitutive relationships. Continuum mechanics deals with the physical properties of solids and fluids which are independent of any particular coordinate sy ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Partial Differential Equations
In mathematics, a partial differential equation (PDE) is an equation which imposes relations between the various partial derivatives of a multivariable function. The function is often thought of as an "unknown" to be solved for, similarly to how is thought of as an unknown number to be solved for in an algebraic equation like . However, it is usually impossible to write down explicit formulas for solutions of partial differential equations. There is, correspondingly, a vast amount of modern mathematical and scientific research on methods to numerically approximate solutions of certain partial differential equations using computers. Partial differential equations also occupy a large sector of pure mathematical research, in which the usual questions are, broadly speaking, on the identification of general qualitative features of solutions of various partial differential equations, such as existence, uniqueness, regularity, and stability. Among the many open questions are the e ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Numerical Differential Equations
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Numerical may refer to: * Number * Numerical digit * Numerical analysis Numerical analysis is the study of algorithms that use numerical approximation (as opposed to symbolic computation, symbolic manipulations) for the problems of mathematical analysis (as distinguished from discrete mathematics). It is the study of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
SAMCEF
SAMCEF is a finite element analysis (FEA) software package dedicated to mechanical virtual prototyping. SAMCEF development started in 1965 at the Aerospace Laboratory of University of Liège. It was developed and sold by SAMTECH, a Belgian company, founded in 1986 and located in Liège, Belgium Belgium, ; french: Belgique ; german: Belgien officially the Kingdom of Belgium, is a country in Northwestern Europe. The country is bordered by the Netherlands to the north, Germany to the east, Luxembourg to the southeast, France to th .... SAMTECH s.a. was acquired by LMS in 2011. LMS was later acquired by Siemens in 2013. SAMCEF is now part of Siemens Simulation Software Simcenter. Software features SAMCEF software package is made of several modules that can be used and bought independently from one another. SAMCEF Field is the package's Graphical User Interface (GUI) where users will define their models based on CAD geometry. SAMCEF Field is able to drive all SAMCEF ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Abaqus
Abaqus FEA (formerly ABAQUS) is a software suite for finite element analysis and computer-aided engineering, originally released in 1978. The name and logo of this software are based on the abacus calculation tool. The Abaqus product suite consists of five core software products: # ''Abaqus/CAE'', or "Complete Abaqus Environment" (a backronym with a root in Computer-Aided Engineering). It is a software application used for both the modeling and analysis of mechanical components and assemblies (pre-processing) and visualizing the finite element analysis result. A subset of Abaqus/CAE including only the post-processing module can be launched independently in the ''Abaqus/Viewer'' product. # ''Abaqus/Standard'', a general-purpose Finite-Element analyzer that employs implicit integration scheme (traditional). # ''Abaqus/Explicit'', a special-purpose Finite-Element analyzer that employs explicit integration scheme to solve highly nonlinear systems with many complex contacts under trans ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
GetFEM++
GetFEM++ is a generic finite element C++ library with interfaces for Python, Matlab and Scilab. It aims at providing finite element methods and elementary matrix computations for solving linear and non-linear problems numerically. Its flexibility in choosing among different finite element approximations and numerical integration methods is one of its distinguishing characteristics. License GetFEM++ is released under the GNU Lesser General Public License, version 3 or later, along with the GCC Runtime Library Exception, version 3.1 or later. Components Gmm++ is a generic matrix template library included in GetFEM++, providing tools for elementary computations with dense and sparse matrices. Among the capabilities implemented in Gmm++ there is also an interface to the popular direct solver for sparse systems of linear equations MUMPS. Mesh objects in GetFEM++ contain information about the geometric transformation and connectivity of mesh elements as well as methods for acc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Partition Of Unity
In mathematics, a partition of unity of a topological space is a set of continuous functions from to the unit interval ,1such that for every point x\in X: * there is a neighbourhood of where all but a finite number of the functions of are 0, and * the sum of all the function values at is 1, i.e., \sum_ \rho(x) = 1. Partitions of unity are useful because they often allow one to extend local constructions to the whole space. They are also important in the interpolation of data, in signal processing, and the theory of spline functions. Existence The existence of partitions of unity assumes two distinct forms: # Given any open cover \_ of a space, there exists a partition \_ indexed ''over the same set'' such that supp \rho_i \subseteq U_i. Such a partition is said to be subordinate to the open cover \_i. # If the space is locally-compact, given any open cover \_ of a space, there exists a partition \_ indexed over a possibly distinct index set such that each has co ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Classical Enriched Nodes1
Classical may refer to: European antiquity *Classical antiquity, a period of history from roughly the 7th or 8th century B.C.E. to the 5th century C.E. centered on the Mediterranean Sea *Classical architecture, architecture derived from Greek and Roman architecture of classical antiquity *Classical mythology, the body of myths from the ancient Greeks and Romans *Classical tradition, the reception of classical Greco-Roman antiquity by later cultures * Classics, study of the language and culture of classical antiquity, particularly its literature *Classicism, a high regard for classical antiquity in the arts Music and arts *Classical ballet, the most formal of the ballet styles * Classical music, a variety of Western musical styles from the 9th century to the present * Classical guitar, a common type of acoustic guitar *Classical Hollywood cinema, a visual and sound style in the American film industry between 1927 and 1963 * Classical Indian dance, various codified art forms whose t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
