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XFEM
The extended finite element method (XFEM), is a numerical technique based on the generalized finite element method (GFEM) and the Partition of unity, 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 (Fracture, 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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Finite Element Method
Finite element method (FEM) is a popular method for numerically solving differential equations arising in engineering and mathematical modeling. Typical problem areas of interest include the traditional fields of structural analysis, heat transfer, fluid flow, mass transport, and electromagnetic potential. Computers are usually used to perform the calculations required. With high-speed supercomputers, better solutions can be achieved and are often required to solve the largest and most complex problems. FEM is a general numerical method for solving partial differential equations in two- or three-space variables (i.e., some boundary value problems). There are also studies about using FEM to solve high-dimensional problems. To solve a problem, FEM subdivides a large system into smaller, simpler parts called finite elements. This is achieved by a particular space discretization in the space dimensions, which is implemented by the construction of a mesh of the object: the numer ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Partial Differential Equations
In mathematics, a partial differential equation (PDE) is an equation which involves a multivariable function and one or more of its partial derivatives. The function is often thought of as an "unknown" that solves the equation, similar to how is thought of as an unknown number solving, e.g., an algebraic equation like . However, it is usually impossible to write down explicit formulae 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 existence an ... [...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 acce ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ted Belytschko
Ted Bohdan Belytschko (January 13, 1943 – September 15, 2014) was an American mechanical engineer. He was Walter P. Murphy Professor and McCormick Professor of Computational Mechanics at Northwestern University. He worked in the field of computational solid mechanics and was known for development of methods like element-free Galerkin method and the Extended finite element method. Belytschko received his B.S. in Engineering Sciences (1965) and his Ph.D. in Mechanics (1968) from the Illinois Institute of Technology. He was named in ISI Database as the fourth most cited engineering researcher in January 2004. He was also the editor of the ''International Journal for Numerical Methods in Engineering''. He died at the age of 71 on September 15, 2014. Awards and honors * William Prager Medal, 2011. *Member of the National Academy of Sciences (2011) *Member of the National Academy of Engineering (1992) * John von Neumann Medal of the United States Association for Computational Mech ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fracture
Fracture is the appearance of a crack or complete separation of an object or material into two or more pieces under the action of stress (mechanics), stress. The fracture of a solid usually occurs due to the development of certain displacement discontinuity surfaces within the solid. If a displacement develops perpendicular to the surface, it is called a normal tensile crack or simply a crack; if a displacement develops tangentially, it is called a shear crack, slip band, or dislocation. #Brittle, Brittle fractures occur without any apparent deformation before fracture. #Ductile, Ductile fractures occur after visible deformation. Fracture strength, or breaking strength, is the stress when a specimen fails or fractures. The detailed understanding of how a fracture occurs and develops in materials is the object of fracture mechanics. Strength Fracture strength, also known as breaking strength, is the stress at which a specimen structural integrity and failure, fails via fra ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Singularity
In mathematics, a singularity is a point at which a given mathematical object is not defined, or a point where the mathematical object ceases to be well-behaved in some particular way, such as by lacking differentiability or analyticity. For example, the reciprocal function f(x) = 1/x has a singularity at x = 0, where the value of the function is not defined, as involving a division by zero. The absolute value function g(x) = , x, also has a singularity at x = 0, since it is not differentiable there. The algebraic curve In mathematics, an affine algebraic plane curve is the zero set of a polynomial in two variables. A projective algebraic plane curve is the zero set in a projective plane of a homogeneous polynomial in three variables. An affine algebraic plane cu ... defined by \left\ in the (x, y) coordinate system has a singularity (called a cusp (singularity), cusp) at (0, 0). For singularities in algebraic geometry, see singular point of an algebraic variety. For singul ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Boundary Layer
In physics and fluid mechanics, a boundary layer is the thin layer of fluid in the immediate vicinity of a Boundary (thermodynamic), bounding surface formed by the fluid flowing along the surface. The fluid's interaction with the wall induces a No-slip condition, no-slip boundary condition (zero velocity at the wall). The flow velocity then monotonically increases above the surface until it returns to the bulk flow velocity. The thin layer consisting of fluid whose velocity has not yet returned to the bulk flow velocity is called the velocity boundary layer. The air next to a human is heated, resulting in gravity-induced convective airflow, which results in both a velocity and thermal boundary layer. A breeze disrupts the boundary layer, and hair and clothing protect it, making the human feel cooler or warmer. On an aircraft wing, the velocity boundary layer is the part of the flow close to the wing, where viscosity, viscous forces distort the surrounding non-viscous flow. In ... [...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 theor ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Partition Of Unity
In mathematics, a partition of unity on a topological space is a Set (mathematics), set of continuous function (topology), continuous functions from to the unit interval [0,1] such that for every point x\in X: * there is a neighbourhood (mathematics), neighbourhood of where all but a finite set, finite number of the functions of are non zero, 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 Support (mathematics), 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 an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Radioss
Altair Radioss is a multidisciplinary finite element solver developed by Altair Engineering. It includes implicit and explicit time integration schemes for the solution of engineering problems, from linearstatics and linear dynamics to non-linear transient dynamics and mechanical systems. The multidisciplinary solver has its main strengths in durability, NVH, crash, safety, manufacturability, and fluid-structure interaction. Since the 2021 release, Radioss has supported input in the LS-DYNA input format as well as the Radioss 'Block' Format OpenRadioss, a source available software version of Radioss, sharing the capabilities, input and output formats of Altair Radioss, was released on September the 8th 2022. Despite being called open source software, the software cannot be compiled or used without a library that is provided only in binary form, and for which third parties are granted "limited permission to use". Disciplines * Linear static analysis * Non-linear explicit dyn ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
