Fiber‐based shakedown analysis of three‐dimensional frames under multiple load combinations: Mixed finite elements and incremental‐iterative solution

We consider mixed finite elements for linear elasticity with weakly symmetric stress. We propose a low-order three-dimensional rectangular element with optimal O(h) rate of convergence for all the unknowns. The element is a rectangular analogue of the simplified Arnold–Falk–Winther element. Instead of the elasticity complex approach, our stability analysis is based on new mesh-dependent norms.

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Computation of the Three-Dimensional Stress State in Composite Shell Structures with Mixed Finite Elements

PAMM ◽

10.1002/pamm.201010101 ◽

2010 ◽

Vol 10 (1) ◽

pp. 217-218

Author(s):

Marco Schürg ◽

Jens Wackerfuß ◽

Friedrich Gruttmann

Keyword(s):

Stress State ◽

Finite Elements ◽

Composite Shell ◽

Three Dimensional ◽

Mixed Finite Elements ◽

Shell Structures

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Application of the iterative solution method with Schur complement reduction to mixed finite elements based in a tetrahedral discretization

Advances in Water Resources ◽

10.1016/j.advwatres.2013.12.006 ◽

2014 ◽

Vol 65 ◽

pp. 9-17 ◽

Cited By ~ 1

Author(s):

Richard L. Naff

Keyword(s):

Finite Elements ◽

Solution Method ◽

Mixed Finite Elements ◽

Schur Complement ◽

Iterative Solution ◽

Iterative Solution Method

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Boundary Condition Design to Heat a Moving Object at Uniform Transient Temperature Using Inverse Formulation

Journal of Manufacturing Science and Engineering ◽

10.1115/1.1763179 ◽

2004 ◽

Vol 126 (3) ◽

pp. 619-626 ◽

Cited By ~ 8

Author(s):

Hakan Ertu¨rk ◽

Ofodike A. Ezekoye ◽

John R. Howell

Keyword(s):

Boundary Condition ◽

Temperature Distribution ◽

Design Problem ◽

Manufacturing Industry ◽

Three Dimensional ◽

Chemical Deposition ◽

Iterative Solution ◽

Conveyor Belt ◽

Temperature History ◽

Transient Temperature

The boundary condition design of a three-dimensional furnace that heats an object moving along a conveyor belt of an assembly line is considered. A furnace of this type can be used by the manufacturing industry for applications such as industrial baking, curing of paint, annealing or manufacturing through chemical deposition. The object that is to be heated moves along the furnace as it is heated following a specified temperature history. The spatial temperature distribution on the object is kept isothermal through the whole process. The temperature distribution of the heaters of the furnace should be changed as the object moves so that the specified temperature history can be satisfied. The design problem is transient where a series of inverse problems are solved. The process furnace considered is in the shape of a rectangular tunnel where the heaters are located on the top and the design object moves along the bottom. The inverse design approach is used for the solution, which is advantageous over a traditional trial-and-error solution where an iterative solution is required for every position as the object moves. The inverse formulation of the design problem is ill-posed and involves a set of Fredholm equations of the first kind. The use of advanced solvers that are able to regularize the resulting system is essential. These include the conjugate gradient method, the truncated singular value decomposition or Tikhonov regularization, rather than an ordinary solver, like Gauss-Seidel or Gauss elimination.

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