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Patch Test (finite Elements)
The patch test in the finite element method is a simple indicator of the quality of a finite element, developed by Bruce Irons (engineer), Bruce Irons. The patch test uses a partial differential equation on a domain consisting from several elements set up so that the exact solution is known and can be reproduced, in principle, with zero error. Typically, in mechanics, the prescribed exact solution consists of displacements that vary as piecewise linear functions in space (called a constant Strain (materials science), strain solution). The elements pass the patch test if the finite element solution is the same as the exact solution. It was long conjectured by engineers that passing the patch test is sufficient for the convergence of the finite element, that is, to ensure that the solutions from the finite element method converge to the exact solution of the partial differential equation as the finite element mesh is refined. However, this is not the case, and the patch test is neithe ... [...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] |
Bruce Irons (engineer)
Bruce Moncur Irons (6 October 1924 – 5 December 1983) was an engineer and mathematician, known for his fundamental contribution to the finite element method, including the patch test, the frontal solver and, along with Ian C. Taig, the isoparametric element concept. He developed multiple sclerosis; finding it difficult to accept anticipated relapses, he committed suicide Suicide is the act of intentionally causing one's own death. Risk factors for suicide include mental disorders, physical disorders, and substance abuse. Some suicides are impulsive acts driven by stress (such as from financial or ac ... on 5 December 1983, and his wife followed suit. References External links Bruce M. Irons Memorial Scholarship 1924 births 20th-century Canadian mathematicians 1983 suicides 1983 deaths Suicides in Alberta {{mathematician-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Partial Differential Equation
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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mechanics
Mechanics () is the area of physics concerned with the relationships between force, matter, and motion among Physical object, physical objects. Forces applied to objects may result in Displacement (vector), displacements, which are changes of an object's position relative to its environment. Theoretical expositions of this branch of physics has its origins in Ancient Greece, for instance, in the writings of Aristotle and Archimedes (see History of classical mechanics and Timeline of classical mechanics). During the early modern period, scientists such as Galileo Galilei, Johannes Kepler, Christiaan Huygens, and Isaac Newton laid the foundation for what is now known as classical mechanics. As a branch of classical physics, mechanics deals with bodies that are either at rest or are moving with velocities significantly less than the speed of light. It can also be defined as the physical science that deals with the motion of and forces on bodies not in the quantum realm. History ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Strain (materials Science)
In mechanics, strain is defined as relative deformation, compared to a position configuration. Different equivalent choices may be made for the expression of a strain field depending on whether it is defined with respect to the initial or the final configuration of the body and on whether the metric tensor or its dual is considered. Strain has dimension of a length ratio, with SI base units of meter per meter (m/m). Hence strains are dimensionless and are usually expressed as a decimal fraction or a percentage. Parts-per notation is also used, e.g., parts per million or parts per billion (sometimes called "microstrains" and "nanostrains", respectively), corresponding to μm/m and nm/m. Strain can be formulated as the spatial derivative of displacement: \boldsymbol \doteq \cfrac\left(\mathbf - \mathbf\right) = \boldsymbol'- \boldsymbol, where is the identity tensor. The displacement of a body may be expressed in the form , where is the reference position of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Butterworth-Heinemann
Butterworth–Heinemann is a British publishing company specialised in professional information and learning materials for higher education and professional training, in printed and electronic forms. It was formed in 1990 by the merger of Heinemann Professional Publishing and Butterworths Scientific, both subsidiaries of Reed International. With its earlier constituent companies, the founding dates back to 1923. It has publishing units in Oxford (UK) and Waltham, Massachusetts (United States). As of 2006, it is an imprint of Elsevier. See also *LexisNexis Butterworths LexisNexis is an American data analytics company headquartered in New York, New York. Its products are various databases that are accessed through online portals, including portals for computer-assisted legal research (CALR), newspaper search, ... References External links * Book publishing companies of the United Kingdom Elsevier imprints {{publish-corp-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Prentice Hall
Prentice Hall was a major American publishing#Textbook_publishing, educational publisher. It published print and digital content for the 6–12 and higher-education market. It was an independent company throughout the bulk of the twentieth century. In its last few years it was owned by, then absorbed into, Savvas Learning Company. In the Web era, it distributed its technical titles through the Safari Books Online e-reference service for some years. History On October 13, 1913, law professor Charles Gerstenberg and his student Richard Ettinger founded Prentice Hall. Gerstenberg and Ettinger took their mothers' maiden names, Prentice and Hall, to name their new company. At the time the name was usually styled as Prentice-Hall (as seen for example on many title pages), per an orthographic norm for Dash#Relationships and connections, coordinate elements within such compounds (compare also ''McGraw-Hill'' with later styling as ''McGraw Hill''). Prentice-Hall became known as a publi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
