" Damage Detection in Bridges using a Mathematical Model by an Updating Method "
Mohammed Lamine MOUSSAOUI , Mohamed CHABAAT , Abderrahmane KIBBOUA
The 9th International Conference on Fracture and Strength of Solids, FEOFS 2013, June 2013, Jeju, South Korea
Status: Accepted
Hi All,
Do you know why some finite element softwares can not solve free-free vibrations of many applications unless you fix at least one degree of freedom ?
In this case I do not see how they are able to analyze free-free structures as planes.
Mohammed Lamine
Which best Describes Structural Damping : Dissipative Energy, Linearization from Stiffness and Mass Matrices, or Strain Energy
Hello,
Some Finite Element Softwares use the Formulation of an Element and Jump to another one
by Merging Nodes : Quadrilateral to Triangular and Hexahedral to Tetrahedral without modifying
the Shape Functions.
This Method is Mathematically and Numericaly Forbidden because they use the Same Shape Functions
when Merging the Nodes for the Defined First Element (see Element Definition and after Mesh Process).
The Simplex K with 4 Vertices in Dimension 3 is a Tetrahedron and :
K = determinant((x2-x1) , (x3-x2) , (x4-x3) ; (y2-y1) , (y3-y2) , (y4-y3) ; (z2-z1) , (z3-z2) , (z4-z3))
The Volume of this element is :
V(K) = abs(K) / 3!
If V(K) ~= 0 then K is Nearly Degenerated
Moussaoui
It is not recommended to Invert a Matrix in Numerical Analysis. Solving with Factorization methods (L.U, L.D.Lt, ..) is better than Solution with Direct Inverse. This is due to Numerical Errors (roundoff) and/or ill-Conditioned problems. In case of you need to use an Inverse, you are advised to take care about using existing algorithms which can't be exact in all applications.
Convergence of Numerical solution may depend on the conditionning of the problem's matrices.
An ill-conditionned matrix produce singulariy cases. This is due to bad shaped elements in
structural mechanics: nearly degenerated elements with zero area (in 2D) or zero volume (in 3D)
The conditionning can be analyzed by numerical algorithms or existing commands in order to
detect these problems.
To avoid the Ambiguity appearing in the Formulation Process using the Numerical Methods of Partial Differentrial Equations it is Important to Satisfy the following Conditions given by Fletcher C.A.J. 1989, p18 :
"The governing Equations and Auxiliary (Initial and Boundary) Conditions are Well-Posed Mathematically if the Following three Condtions are met:
