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Jacobian Calculation

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hi sir, i have one doubt, how does the hypermesh calculates the jacobian value for an element?. i have searched many but i could find only the definition.

Dhinesh

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Hi Dhinesh,

The Jacobian ratio is a measure of the deviation of a given element from an ideally shaped element. The Jacobian value ranges from -1.0 to 1.0, where 1.0 represents a perfectly shaped element. The ideal shape for an element depends on the element type. The check is performed by mapping an ideal element in parametric coordinates onto the actual element defined in global coordinates. For example, the coordinates of the corners of an ideal quad element in parametric coordinates are (-1,- 1), (1,-1), (1,1), and (-1,1). The determinant of the Jacobian relates the local stretching of the parametric space required to "t it onto global coordinate space. HyperMesh evaluates the determinant of the Jacobian matrix at each of the element’s integration points (also called Gauss points), and reports the ratio between the smallest and the largest. If the local stretching is the same at all of its Gauss points, then the Jacobian value equals 1.0. As the element becomes more distorted, the Jacobian value approaches zero. A Jacobian value of less than zero represents a concave element, which most analysis codes do not allow.

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Hi,

An integration point is the point within an element at which integrals are evaluated numerically. These points are chosen in such a way that the results for a particular numerical integration scheme are the most accurate.Gauss quadrature is a means for numerical integration, which evaluates an integral as the sum of a finite number of terms, and such calculated element’s integration points are called as Gauss points. Reduced integration method uses a lesser number of Gaussian co-ordinates when solving the integral. Clearly, the more Gaussian co-ordinates you have for each element, the more accurate your answer will be, but at the cost of computation time.

There are many open web sources and books available on numerical integration methods which will give you more information on the same. Also, I suggest you to go through Altair's Learning Program on Learning CAE Fundamentals, where these concepts are covered. You can access the Learning Program at : http://certification.altairuniversity.com

 

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Sir,

 

Which open web sources and books will give complete detailed about FEA. Because many book have not include all those thing even  Learning Program at : http://certification.altairuniversity.com  will provide basic knowledge. Will you suggest any website or book will give detailed knowledge of all this thing. I had also read FEA by Altair (practical aspect)

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Hi Hari,

There are many good books and web resources (YouTube channels also) on Finite Element Analysis. 

Please refer http://www.altairuniversity.com/2039-lecture-series-on-finite-element-method-by-prof-c-s-uppadhay-department-of-aero-space-iit-kanpur/ which is a lecture series on Finite Element Methods. I can suggest you Finite Ele ment Analysis Formulation, Verification and Validation book by Szabó and Babuška which covers many aspects.

In Altair Learning program for CAE Fundamentals we have covered the basics on FEA including Interpolation Functions, Stiffness Matrices,Approximation....etc which will be a good package for a beginner to start on Finite Element Analysis.

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