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
The 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 t ...
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
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 wat ...
for the determination of collapse loads for geotechnical problems (e.g.
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 i ...
). An alternative technique which may be used to undertake similar direct plastic collapse computations using optimization is
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 'dis ...
.
Software for finite element limit analysis
OptumG2(2014-) General purpose software for 2D geotechnical applications.
OptumG3(2017-) General purpose software for 3D geotechnical applications.
See also
*
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 t ...
References
Further reading
* Kumar, Jyant, and Debasis Mohapatra. "Lower-bound finite elements limit analysis for Hoek-Brown materials using semidefinite programming." Journal of Engineering Mechanics 143.9 (2017): 04017077.
* Makrodimopoulos, A., and C. M. Martin. "Lower bound limit analysis of cohesive‐frictional materials using second‐order cone programming." International Journal for Numerical Methods in Engineering 66.4 (2006): 604-634.
* Kumar, Jyant, and Vishwas N. Khatri.
Bearing capacity factors of circular foundations for a general c–ϕ soil using lower bound finite elements limit analysis" International Journal for Numerical and Analytical Methods in Geomechanics 35.3 (2011): 393-405.
* Tang, Chong, Kim-Chuan Toh, and Kok-Kwang Phoon.
Axisymmetric lower-bound limit analysis using finite elements and second-order cone programming" Journal of Engineering Mechanics 140.2 (2013): 268-278.
* Kumar, Jyant, and Obaidur Rahaman.
Vertical uplift resistance of horizontal plate anchors for eccentric and inclined loads" Canadian Geotechnical Journal(2018).
* Mohapatra D, Kumar J. Collapse loads for rectangular foundations by three‐dimensional upper bound limit analysis using radial point interpolation method. Int J Numer Anal Methods Geomech. 2018;1–20. https://doi.org/10.1002/nag.2885
{{DEFAULTSORT:Finite element limit analysis
Structural analysis
Soil mechanics