mohammedlamine's blog

Hello,

The attached file describes the development of the transformation matrix of a beam element:

The composite strength of Reinforced Concrete which is a mixture of two main materials can be calculated by the formula given by Tsai : X=(vf+vm*Em/Ef)*Xf  where vf is the fiber (steel) fraction and vm is the concrete (cement+sands+gravels) fraction. Xf is the yield strength of Steel and Xm is the compressive strength of the Concrete matrix. For the application case: vf=0.01911, vm=0.98089, Xf=270 MPa, Xm=40 MPa, Ef=207.000 GPa, Em=30.798 GPa we obtain X=44.563 MPa.

Hello,

The problem in numerics is the neutralization of the errors for example plus (+)error and minus (-)error. For that reason it is difficult to locate a convergent process. Some numerical algorithms avoid these omissions like leat squares methods which handle the square of the errors in the minimization function. In the other applications like solving processes truncating errors and roundoff errors can be analyzed successfully.

Hello,

I have developped a New Method to Compute Numerically the Shape Functions of a Constant Strain Tetrahedron from the Geometrical Information of its Vertices using the Planes' Equations Defining the Barycentric Coordinates versus the Cartesian Coordinates. The Algorithm for Solving the Linear Systems of Equations has been Implemented Efficiently with the Partial Pivoting Gauss LU Method for any arbitrary Shaped and Non-Degenerated Element.

References: FEOFS2013, CanCNSM2013 and FDM2013.

Best Regards.

Hi all,

Here are the references of the following technical publication: 

Title: " Dynamic Detection of Reinforced Concrete Bridge Damages by Finite Element Model Updating ".

Author(s) : Mohammed Lamine MOUSSAOUI, Mohamed CHABAAT, Abderrahmane KIBBOUA.

Area: Non-Smooth Vibrations in Structural Dynamics II.

Conference: 4th Canadian Conference on Nonlinear Solid Mechanics (CanCNSM 2013)

Location: McGill University, Montreal, Canada

Date: July 23-26, 2013

Status: Accepted / Done

Hi all,

There are several formulae allowing the computation of tetrahedral volume elements. The weakness of some of them is that they give negative volumes. This is due to the vector dot product and its direction. You must take care when using them.

You have to check your formula with some simple examples like the vertices of the following one: (1,0,0) , (0,1,0) , (0,0,1) , (0,0,0). 

Mohammed lamine Moussaoui 

The Solution of a Differential Equation or a Set of Differential Equations Converges vers the Exact if it is Consistant and it is Stable : Lax's Theorem. Since the Exact is not always known it is convenient to apply this Theorem. Numerical instabilities are a result of Roundoff errors and Truncation errors. The Domain of Stability can be obtained from a Von Newman analysis in the Complex domain. This implies a condition (relation) between the variation steps. 

Mohammed Lamine