FEM software provides a wide range of simulation options for controlling the complexity of both modeling and analysis of a system. Similarly, the desired level of accuracy required and associated computational time requirements can be managed simultaneously to address most engineering applications.
FEM allows entire designs to be constructed, refined, and optimized before the design is manufactured. The mesh is an integral part of the model and it must be controlled carefully to give the best results. Generally the higher the number of elements in a mesh, the more accurate the solution of the discretised problem.
However, there is a value at which the results converge and further mesh refinement does not increase accuracy. This powerful design tool has significantly improved both the standard of engineering designs and the methodology of the design process in many industrial applications. In the s FEA was proposed for use in stochastic modelling for numerically solving probability models  and later for reliability assessment.
From Wikipedia, the free encyclopedia. Numerical method for solving physical or engineering problems. For the elements of a poset , see compact element. Navier—Stokes differential equations used to simulate airflow around an obstruction.
Natural sciences Engineering. Order Operator. Relation to processes. Difference discrete analogue Stochastic Stochastic partial Delay.
In order to meet the requirements of solution verification, postprocessors need to provide for a posteriori error estimation in terms of the quantities of interest. One hopes that as the underlying triangular mesh becomes finer and finer, the solution of the discrete problem 3 will in some sense converge to the solution of the original boundary value problem P2. Design Optimization. Chetan Jadhav rated it really liked it Oct 31, It was developed by combining meshfree methods with the finite element method. Kooky rated it it was amazing Sep 08,
General topics. Phase portrait Phase space. Numerical integration Dirac delta function.
Solution methods. Colours indicate that the analyst has set material properties for each zone, in this case a conducting wire coil in orange; a ferromagnetic component perhaps iron in light blue; and air in grey. Although the geometry may seem simple, it would be very challenging to calculate the magnetic field for this setup without FEM software, using equations alone. FEM solution to the problem at left, involving a cylindrically shaped magnetic shield. The ferromagnetic cylindrical part is shielding the area inside the cylinder by diverting the magnetic field created by the coil rectangular area on the right.
The color represents the amplitude of the magnetic flux density , as indicated by the scale in the inset legend, red being high amplitude. The area inside the cylinder is low amplitude dark blue, with widely spaced lines of magnetic flux , which suggests that the shield is performing as it was designed to. Interpolation of a Bessel function. The linear combination of basis functions yellow reproduces J 0 blue to any desired accuracy.
Main article: Applied element method.
Main article: Mixed finite element method. Main article: Extended finite element method. Main article: Smoothed finite element method. Main article: Spectral element method. Main article: Meshfree methods. Main article: Discontinuous Galerkin method. Main article: Finite element limit analysis.
Main article: Stretched grid method. This section does not cite any sources. Please help improve this section by adding citations to reliable sources. Unsourced material may be challenged and removed. November Learn how and when to remove this template message. Logan A first course in the finite element method.
Cengage Learning. Retrieved Journal of Applied Mechanics. Bulletin of the American Mathematical Society. Retrieved 17 March Prentice Hall. Zhu 31 August Finite Element Procedures. Programming the Finite Element Method Fifth ed. June International Journal of Computational Methods.
Solin, K. Segeth, I.
Computer Methods in Applied Mechanics and Engineering. Machine Design. Coventive Composites. Archived from the original on Journal of Computational and Applied Mathematics.
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