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Signorini Problem
The Signorini problem is an elastostatics problem in linear elasticity: it consists in finding the elastic equilibrium configuration of an anisotropic non-homogeneous elastic body, resting on a rigid frictionless surface and subject only to its mass forces. The name was coined by Gaetano Fichera to honour his teacher, Antonio Signorini: the original name coined by him is problem with ambiguous boundary conditions. History The problem was posed by Antonio Signorini during a course taught at the '' Istituto Nazionale di Alta Matematica'' in 1959, later published as the article , expanding a previous short exposition he gave in a note published in 1933. himself called it ''problem with ambiguous boundary conditions'', since there are two alternative sets of boundary conditions the solution ''must satisfy'' on any given contact point. The statement of the problem involves not only equalities ''but also inequalities'', and ''it is not a priori known what of the two se ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Linear Elasticity
Linear elasticity is a mathematical model of how solid objects deform and become internally stressed due to prescribed loading conditions. It is a simplification of the more general nonlinear theory of elasticity and a branch of continuum mechanics. The fundamental "linearizing" assumptions of linear elasticity are: infinitesimal strains or "small" deformations (or strains) and linear relationships between the components of stress and strain. In addition linear elasticity is valid only for stress states that do not produce yielding. These assumptions are reasonable for many engineering materials and engineering design scenarios. Linear elasticity is therefore used extensively in structural analysis and engineering design, often with the aid of finite element analysis. Mathematical formulation Equations governing a linear elastic boundary value problem are based on three tensor partial differential equations for the balance of linear momentum and six infinitesimal strain- ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Inequality (mathematics)
In mathematics, an inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions. It is used most often to compare two numbers on the number line by their size. There are several different notations used to represent different kinds of inequalities: * The notation ''a'' ''b'' means that ''a'' is greater than ''b''. In either case, ''a'' is not equal to ''b''. These relations are known as strict inequalities, meaning that ''a'' is strictly less than or strictly greater than ''b''. Equivalence is excluded. In contrast to strict inequalities, there are two types of inequality relations that are not strict: * The notation ''a'' ≤ ''b'' or ''a'' ⩽ ''b'' means that ''a'' is less than or equal to ''b'' (or, equivalently, at most ''b'', or not greater than ''b''). * The notation ''a'' ≥ ''b'' or ''a'' ⩾ ''b'' means that ''a'' is greater than or equal to ''b'' (or, equivalently, at least ''b'', or not less than ''b''). The re ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dimension
In physics and mathematics, the dimension of a Space (mathematics), mathematical space (or object) is informally defined as the minimum number of coordinates needed to specify any Point (geometry), point within it. Thus, a Line (geometry), line has a dimension of one (1D) because only one coordinate is needed to specify a point on itfor example, the point at 5 on a number line. A Surface (mathematics), surface, such as the Boundary (mathematics), boundary of a Cylinder (geometry), cylinder or sphere, has a dimension of two (2D) because two coordinates are needed to specify a point on itfor example, both a latitude and longitude are required to locate a point on the surface of a sphere. A two-dimensional Euclidean space is a two-dimensional space on the Euclidean plane, plane. The inside of a cube, a cylinder or a sphere is three-dimensional (3D) because three coordinates are needed to locate a point within these spaces. In classical mechanics, space and time are different categ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Subset
In mathematics, Set (mathematics), set ''A'' is a subset of a set ''B'' if all Element (mathematics), elements of ''A'' are also elements of ''B''; ''B'' is then a superset of ''A''. It is possible for ''A'' and ''B'' to be equal; if they are unequal, then ''A'' is a proper subset of ''B''. The relationship of one set being a subset of another is called inclusion (or sometimes containment). ''A'' is a subset of ''B'' may also be expressed as ''B'' includes (or contains) ''A'' or ''A'' is included (or contained) in ''B''. A ''k''-subset is a subset with ''k'' elements. The subset relation defines a partial order on sets. In fact, the subsets of a given set form a Boolean algebra (structure), Boolean algebra under the subset relation, in which the join and meet are given by Intersection (set theory), intersection and Union (set theory), union, and the subset relation itself is the Inclusion (Boolean algebra), Boolean inclusion relation. Definition If ''A'' and ''B'' are sets and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Displacement Vector
In geometry and mechanics, a displacement is a vector whose length is the shortest distance from the initial to the final position of a point P undergoing motion. It quantifies both the distance and direction of the net or total motion along a straight line from the initial position to the final position of the point trajectory. A displacement may be identified with the translation that maps the initial position to the final position. A displacement may be also described as a '' relative position'' (resulting from the motion), that is, as the final position of a point relative to its initial position . The corresponding displacement vector can be defined as the difference between the final and initial positions: s = x_\textrm - x_\textrm = \Delta In considering motions of objects over time, the instantaneous velocity of the object is the rate of change of the displacement as a function of time. The instantaneous speed, then, is distinct from velocity, or the time rate of chan ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Variational Inequality
In mathematics, a variational inequality is an inequality involving a functional, which has to be solved for all possible values of a given variable, belonging usually to a convex set. The mathematical theory of variational inequalities was initially developed to deal with equilibrium problems, precisely the Signorini problem: in that model problem, the functional involved was obtained as the first variation of the involved potential energy. Therefore, it has a variational origin, recalled by the name of the general abstract problem. The applicability of the theory has since been expanded to include problems from economics, finance, optimization and game theory. History The first problem involving a variational inequality was the Signorini problem, posed by Antonio Signorini in 1959 and solved by Gaetano Fichera in 1963, according to the references and : the first papers of the theory were and , . Later on, Guido Stampacchia proved his generalization to the Lax–Milgram the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Family Doctor
Family medicine is a medical specialty within primary care that provides continuing and comprehensive health care for the individual and family across all ages, genders, diseases, and parts of the body. The specialist, who is usually a primary care physician, is named a family physician. It is often referred to as general practice and a practitioner as a general practitioner. Historically, their role was once performed by any doctor with qualifications from a medical school and who works in the community. However, since the 1950s, family medicine / general practice has become a specialty in its own right, with specific training requirements tailored to each country. The names of the specialty emphasize its holistic nature and/or its roots in the family. It is based on knowledge of the patient in the context of the family and the community, focusing on disease prevention and health promotion. According to the World Organization of Family Doctors (WONCA), the aim of family medic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Virtual Work Principle
D'Alembert's principle, also known as the Lagrange–d'Alembert principle, is a statement of the fundamental classical laws of motion. It is named after its discoverer, the French physicist and mathematician Jean le Rond d'Alembert. D'Alembert's principle generalizes the principle of virtual work from static to dynamical systems by introducing ''forces of inertia'' which, when added to the applied forces in a system, result in ''dynamic equilibrium''. The principle does not apply for irreversible displacements, such as sliding friction, and more general specification of the irreversibility is required. D'Alembert's principle is more general than Hamilton's principle as it is not restricted to holonomic constraints that depend only on coordinates and time but not on velocities. Statement of the principle The principle states that the sum of the differences between the forces acting on a system of massive particles and the time derivatives of the momenta of the system itself p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
First Principle
In philosophy and science, a first principle is a basic proposition or assumption that cannot be deduced from any other proposition or assumption. First principles in philosophy are from First Cause attitudes and taught by Aristotelians, and nuanced versions of first principles are referred to as postulates by Kantians. In mathematics, first principles are referred to as axioms or postulates. In physics and other sciences, theoretical work is said to be from first principles, or ''ab initio'', if it starts directly at the level of established science and does not make assumptions such as empirical model and parameter fitting. "First principles thinking" consists of deriving things to their fundamental proven axioms in the given arena, before reasoning up by asking which ones are relevant to the question at hand, then cross referencing conclusions based on chosen axioms and making sure conclusions do not violate any fundamental laws. Physicists include counterintuitive concepts with ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Boundary Value Problem
In mathematics, in the field of differential equations, a boundary value problem is a differential equation together with a set of additional constraints, called the boundary conditions. A solution to a boundary value problem is a solution to the differential equation which also satisfies the boundary conditions. Boundary value problems arise in several branches of physics as any physical differential equation will have them. Problems involving the wave equation, such as the determination of normal modes, are often stated as boundary value problems. A large class of important boundary value problems are the Sturm–Liouville problems. The analysis of these problems involves the eigenfunctions of a differential operator. To be useful in applications, a boundary value problem should be well posed. This means that given the input to the problem there exists a unique solution, which depends continuously on the input. Much theoretical work in the field of partial differential ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mauro Picone
Mauro Picone (2 May 1885 – 11 April 1977) was an Italian mathematician. He is known for the Picone identity, the Sturm-Picone comparison theorem and being the founder of the Istituto per le Applicazioni del Calcolo, presently named after him, the first applied mathematics institute ever founded.See , , and the references cited in this latter one. He was also an outstanding teacher of mathematical analysis: some of the best Italian mathematicians were among his pupils. Work Research activity Teaching activity Notable students: *Luigi Amerio *Renato Caccioppoli *Gianfranco Cimmino * Ennio de Giorgi *Gaetano Fichera *Carlo Miranda Selected publications * (Review of the whole volume I) (available from the "Edizione Nazionale Mathematica Italiana'"), reviewed by . *, (Review of the 2nd part of volume I) (available from the "Edizione Nazionale Mathematica Italiana'"). *, reviewed by and by . See also *Renato Caccioppoli *Lamberto Cesari * Ennio de Giorgi *Gaetano Fichera ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
