Finite Element Limit Analysis

	Finite Element Limit Analysis A finite element limit analysis (FELA) uses optimisation techniques to directly compute the upper or lower bound plastic collapse load (or limit load) for a mechanical system rather than time stepping to a collapse load, as might be undertaken with conventional non-linear finite element techniques. The problem may be formulated in either a kinematic or equilibrium form.Sloan, S. (1988). Lower bound limit analysis using finite elements and linear programming. Int. J. Num. Anal. Meth. in Geomech. 12(4), 61–77. The technique has been used most significantly in the field of soil mechanics for the determination of collapse loads for geotechnical problems (e.g. slope stability analysis). An alternative technique which may be used to undertake similar direct plastic collapse computations using optimization is Discontinuity layout optimization. Software for finite element limit analysis OptumG2(2014-) General purpose software for 2D geotechnical applications. OptumG3(2017-) General purp ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
picture info	Optimization (mathematics) Mathematical optimization (alternatively spelled ''optimisation'') or mathematical programming is the selection of a best element, with regard to some criterion, from some set of available alternatives. It is generally divided into two subfields: discrete optimization and continuous optimization. Optimization problems of sorts arise in all quantitative disciplines from computer science and engineering to operations research and economics, and the development of solution methods has been of interest in mathematics for centuries. In the more general approach, an optimization problem consists of maximizing or minimizing a real function by systematically choosing input values from within an allowed set and computing the value of the function. The generalization of optimization theory and techniques to other formulations constitutes a large area of applied mathematics. More generally, optimization includes finding "best available" values of some objective function given a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
	Limit Loads Limit load is the maximum load that a structure can safely carry. It's the load at which the structure is in a state of incipient plastic collapse. As the load on the structure increases, the displacements increases linearly in the elastic range until the load attains the yield value. Beyond this, the load-displacement response becomes non-linear and the plastic or irreversible part of the displacement increases steadily with the applied load. Plasticity spreads throughout the solid and at the limit load, the plastic zone becomes very large and the displacements become unbounded and the component is said to have collapsed. Any load above the limit load will lead to the formation of plastic hinge in the structure. Engineers use limit states to define and check a structure's performance. Bounding Theorems of Plastic-Limit Load Analysis: Plastic limit theorems provide a way to calculate limit loads without having to solve the boundary value problem in continuum mechanics. Finite eleme ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
picture info	Finite Element The finite element method (FEM) is a popular method for numerically solving differential equations arising in engineering and mathematical models, mathematical modeling. Typical problem areas of interest include the traditional fields of structural analysis, heat transfer, fluid flow, mass transport, and electromagnetic potential. The FEM is a general numerical analysis, numerical method for solving partial differential equations in two or three space variables (i.e., some boundary value problems). To solve a problem, the FEM subdivides a large system into smaller, simpler parts that are called finite elements. This is achieved by a particular space discretization in the space dimensions, which is implemented by the construction of a Types of mesh, mesh of the object: the numerical domain for the solution, which has a finite number of points. The finite element method formulation of a boundary value problem finally results in a system of algebraic equations. The method approxi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
picture info	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 soi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
picture info	Slope Stability Analysis Slope stability analysis is a static or dynamic, analytical or empirical method to evaluate the stability of earth and rock-fill dams, embankments, excavated slopes, and natural slopes in soil and rock. Slope stability refers to the condition of inclined soil or rock slopes to withstand or undergo movement. The stability condition of slopes is a subject of study and research in soil mechanics, geotechnical engineering and engineering geology. Analyses are generally aimed at understanding the causes of an occurred slope failure, or the factors that can potentially trigger a slope movement, resulting in a landslide, as well as at preventing the initiation of such movement, slowing it down or arresting it through mitigation countermeasures. The stability of a slope is essentially controlled by the ratio between the available shear strength and the acting shear stress, which can be expressed in terms of a safety factor if these quantities are integrated over a potential (or actual) s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
picture info	Discontinuity Layout Optimization Discontinuity layout optimization (DLO) is an engineering analysis procedure which can be used to directly establish the amount of load that can be carried by a solid or structure prior to collapse. Using DLO the layout of failure planes, or 'discontinuities', in a collapsing solid or structure are identified using mathematical optimization methods (hence the name, 'discontinuity layout optimization'). It is assumed that failure occurs in a ductile or 'plastic' manner. How it works The DLO procedure involves a number of steps, as outlined below. The set of potential discontinuities can include discontinuities which crossover one another, allowing complex failure patterns to be identified (e.g. involving ‘fan’ mechanisms, where many discontinuities radiate from a point). DLO can be formulated in terms of equilibrium relations ('static' formulation) or in terms of displacements ('kinematic' formulation). In the latter case the objective of the mathematical optimization proble ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
	Limit Analysis Limit analysis is a structural analysis field which is dedicated to the development of efficient methods to directly determine estimates of the collapse load of a given structural model without resorting to iterative or incremental analysis. For this purpose, the field of limit analysis is based on a set of theorems, referred to as limit theorems, which are a set of theorems based on the law of conservation of energy In physics and chemistry, the law of conservation of energy states that the total energy of an isolated system remains constant; it is said to be ''conserved'' over time. This law, first proposed and tested by Émilie du Châtelet, means that ... that state properties regarding stresses and strains, lower and upper-bound limits for the collapse load and the exact collapse load. Software for limit analysis OPTUM G2(2014-) General purpose software for geotechnical applications in 2D (also includes elastoplasticity, seepage, consolidation, staged construction, tunne ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
	Structural Analysis Structural analysis is a branch of Solid Mechanics which uses simplified models for solids like bars, beams and shells for engineering decision making. Its main objective is to determine the effect of loads on the physical structures and their components. In contrast to theory of elasticity, the models used in structure analysis are often differential equations in one spatial variable. Structures subject to this type of analysis include all that must withstand loads, such as buildings, bridges, aircraft and ships. Structural analysis uses ideas from applied mechanics, materials science and applied mathematics to compute a structure's deformations, internal forces, stresses, support reactions, velocity, accelerations, and stability. The results of the analysis are used to verify a structure's fitness for use, often precluding physical tests. Structural analysis is thus a key part of the engineering design of structures. [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]