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Material Point Method
The material point method (MPM) is a numerical technique used to simulate the behavior of solids, liquids, gases, and any other continuum material. Especially, it is a robust spatial discretization method for simulating multi-phase (solid-fluid-gas) interactions. In the MPM, a continuum body is described by a number of small Lagrangian elements referred to as 'material points'. These material points are surrounded by a background mesh/grid that is used to calculate terms such as the deformation gradient. Unlike other mesh-based methods like the finite element method, finite volume method or finite difference method, the MPM is not a mesh based method and is instead categorized as a meshless/meshfree or continuum-based particle method, examples of which are smoothed particle hydrodynamics and peridynamics. Despite the presence of a background mesh, the MPM does not encounter the drawbacks of mesh-based methods (high deformation tangling, advection errors etc.) which makes it a promisi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Solid
Solid is one of the State of matter#Four fundamental states, four fundamental states of matter (the others being liquid, gas, and Plasma (physics), plasma). The molecules in a solid are closely packed together and contain the least amount of kinetic energy. A solid is characterized by structural rigidity and resistance to a force applied to the surface. Unlike a liquid, a solid object does not flow to take on the shape of its container, nor does it expand to fill the entire available volume like a gas. The atoms in a solid are bound to each other, either in a regular geometric lattice (crystal, crystalline solids, which include metals and ordinary ice), or irregularly (an amorphous solid such as common window glass). Solids cannot be compressed with little pressure whereas gases can be compressed with little pressure because the molecules in a gas are loosely packed. The branch of physics that deals with solids is called solid-state physics, and is the main branch of condens ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Infinitesimal Strain Theory
In continuum mechanics, the infinitesimal strain theory is a mathematical approach to the description of the deformation of a solid body in which the displacements of the material particles are assumed to be much smaller (indeed, infinitesimally smaller) than any relevant dimension of the body; so that its geometry and the constitutive properties of the material (such as density and stiffness) at each point of space can be assumed to be unchanged by the deformation. With this assumption, the equations of continuum mechanics are considerably simplified. This approach may also be called small deformation theory, small displacement theory, or small displacement-gradient theory. It is contrasted with the finite strain theory where the opposite assumption is made. The infinitesimal strain theory is commonly adopted in civil and mechanical engineering for the stress analysis of structures built from relatively stiff elastic materials like concrete and steel, since a common goal in t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Partial Differential Equation
In mathematics, a partial differential equation (PDE) is an equation which imposes relations between the various partial derivatives of a Multivariable calculus, 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 Numerical methods for partial differential equations, numerically approximate solutions of certain partial differential equations using computers. Partial differential equations also occupy a large sector of pure mathematics, 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 a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lagrangian And Eulerian Coordinates
__NOTOC__ In classical field theories, the Lagrangian specification of the flow field is a way of looking at fluid motion where the observer follows an individual fluid parcel as it moves through space and time. Plotting the position of an individual parcel through time gives the pathline of the parcel. This can be visualized as sitting in a boat and drifting down a river. The Eulerian specification of the flow field is a way of looking at fluid motion that focuses on specific locations in the space through which the fluid flows as time passes. This can be visualized by sitting on the bank of a river and watching the water pass the fixed location. The Lagrangian and Eulerian specifications of the flow field are sometimes loosely denoted as the Lagrangian and Eulerian frame of reference. However, in general both the Lagrangian and Eulerian specification of the flow field can be applied in any observer's frame of reference, and in any coordinate system used within the chosen fra ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Arbitrary Lagrangian Eulerian
Arbitrariness is the quality of being "determined by chance, whim, or impulse, and not by necessity, reason, or principle". It is also used to refer to a choice made without any specific criterion or restraint. Arbitrary decisions are not necessarily the same as random decisions. For example, during the 1973 oil crisis, Americans were allowed to purchase gasoline only on odd-numbered days if their license plate was odd, and on even-numbered days if their license plate was even. The system was well-defined and not random in its restrictions; however, since license plate numbers are completely unrelated to a person's fitness to purchase gasoline, it was still an arbitrary division of people. Similarly, schoolchildren are often organized by their surname in alphabetical order, a non-random yet an arbitrary method—at least in cases where surnames are irrelevant. Philosophy Arbitrary actions are closely related to teleology, the study of purpose. Actions lacking a ''telos'', a go ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Meshfree Methods
In the field of numerical analysis, meshfree methods are those that do not require connection between nodes of the simulation domain, i.e. a mesh, but are rather based on interaction of each node with all its neighbors. As a consequence, original extensive properties such as mass or kinetic energy are no longer assigned to mesh elements but rather to the single nodes. Meshfree methods enable the simulation of some otherwise difficult types of problems, at the cost of extra computing time and programming effort. The absence of a mesh allows Lagrangian simulations, in which the nodes can move according to the velocity field. Motivation Numerical methods such as the finite difference method, finite-volume method, and finite element method were originally defined on meshes of data points. In such a mesh, each point has a fixed number of predefined neighbors, and this connectivity between neighbors can be used to define mathematical operators like the derivative. These operators are t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Snow
Snow comprises individual ice crystals that grow while suspended in the atmosphere—usually within clouds—and then fall, accumulating on the ground where they undergo further changes. It consists of frozen crystalline water throughout its life cycle, starting when, under suitable conditions, the ice crystals form in the atmosphere, increase to millimeter size, precipitate and accumulate on surfaces, then metamorphose in place, and ultimately melt, slide or sublimate away. Snowstorms organize and develop by feeding on sources of atmospheric moisture and cold air. Snowflakes nucleate around particles in the atmosphere by attracting supercooled water droplets, which freeze in hexagonal-shaped crystals. Snowflakes take on a variety of shapes, basic among these are platelets, needles, columns and rime. As snow accumulates into a snowpack, it may blow into drifts. Over time, accumulated snow metamorphoses, by sintering, sublimation and freeze-thaw. Where the climate is co ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Walt Disney Animation Studios
Walt Disney Animation Studios (WDAS), sometimes shortened to Disney Animation, is an American animation studio that creates animated features and short films for The Walt Disney Company. The studio's current production logo features a scene from its first synchronized sound cartoon, ''Steamboat Willie'' (1928). Founded on October 16, 1923, by brothers Walt Disney and Roy O. Disney, it is the oldest-running animation studio in the world. It is currently organized as a division of Walt Disney Studios and is headquartered at the Roy E. Disney Animation Building at the Walt Disney Studios lot in Burbank, California. Since its foundation, the studio has produced 61 feature films, from '' Snow White and the Seven Dwarfs'' (1937) to '' Strange World'' (2022), and hundreds of short films. The animation studio (and its parent company) indirectly takes its name from Isigny-sur-Mer, in Calvados, Normandy, France, where Disney's ancestors were based there for a few years. Founded as D ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Corvallis, OR
Corvallis ( ) is a city and the county seat of Benton County in central western Oregon, United States. It is the principal city of the Corvallis, Oregon Metropolitan Statistical Area, which encompasses all of Benton County. As of the 2020 United States Census, the population was 59,922. Corvallis is the location of Oregon State University and Good Samaritan Regional Medical Center. Corvallis is the westernmost city in the contiguous 48 states with a population larger than 50,000. History Establishment In October 1845, Joseph C. Avery arrived in Oregon from the east.David D. Fagan''History of Benton County, Oregon: Including... a Full Political History, ...Incidents of Pioneer Life, and Biographical Sketches of Early and Prominent Citizens...''Portland, OR: A.G. Walling, Printer, 1885; pg. 422. Note that a clear typographical error in the original source has Avery's date of arrival as "October 1846", but beginning of his residence in "June 1846." Avery took out a land claim a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Soil Mechanics
Soil mechanics is a branch of soil physics and applied mechanics that describes the behavior of soils. It differs from fluid mechanics and solid mechanics in the sense that soils consist of a heterogeneous mixture of fluids (usually air and water) and particles (usually clay, silt, sand, and gravel) but soil may also contain organic solids and other matter.Mitchell, J.K., and Soga, K. (2005) Fundamentals of soil behavior, Third edition, John Wiley and Sons, Inc., .Powrie, W., Spon Press, 2004, ''Soil Mechanics – 2nd ed'' A Guide to Soil Mechanics, Bolton, Malcolm, Macmillan Press, 1979. Along with rock mechanics, soil mechanics provides the theoretical basis for analysis in geotechnical engineering, a subdiscipline of civil engineering, and engineering geology, a subdiscipline of geology. Soil mechanics is used to analyze the deformations of and flow of fluids within natural and man-made structures that are supported on or made of soil, or structures that are buried in soils.L ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Geotechnical Engineering
Geotechnical engineering is the branch of civil engineering concerned with the engineering behavior of earth materials. It uses the principles of soil mechanics and rock mechanics for the solution of its respective engineering problems. It also relies on knowledge of geology, hydrology, geophysics, and other related sciences. Geotechnical (rock) engineering is a subdiscipline of geological engineering. In addition to civil engineering, geotechnical engineering also has applications in military, mining, petroleum, coastal engineering, and offshore construction. The fields of geotechnical engineering and engineering geology have knowledge areas that overlap, however, while geotechnical engineering is a specialty of civil engineering, engineering geology is a specialty of geology: They share the same principles of soil mechanics and rock mechanics, but differ in the application. History Humans have historically used soil as a material for flood control, irrigation purposes, buria ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Los Alamos National Laboratory
Los Alamos National Laboratory (often shortened as Los Alamos and LANL) is one of the sixteen research and development laboratories of the United States Department of Energy (DOE), located a short distance northwest of Santa Fe, New Mexico, in the American southwest. Best known for its central role in helping develop the first atomic bomb, LANL is one of the world's largest and most advanced scientific institutions. Los Alamos was established in 1943 as Project Y, a top-secret site for designing nuclear weapons under the Manhattan Project during World War II.The site was variously called Los Alamos Laboratory and Los Alamos Scientific Laboratory. Chosen for its remote yet relatively accessible location, it served as the main hub for conducting and coordinating nuclear research, bringing together some of the world's most famous scientists, among them numerous Nobel Prize winners. The town of Los Alamos, directly north of the lab, grew extensively through this period. After ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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