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Subject: Re: Hex & Tet elements
Author: William Scott Zemitis
Date: 1998-12-14 12:39:00Aside from the other factors mentioned, another consideration which confuses
the issue of tet vs. brick superiority is the completeness of the polynomial
describing the displacement functions of each type of element.
For example, the 10 terms in the displacement function for the 10-noded tet
element represents a complete 2nd order polynomial. The 8-noded brick
displacement function, while lacking several of the second order terms of
the 10-noded tet, has a third order term (xyz) absent in the tet. Likewise,
though the 20-noded brick is a "quadratic" element like the 10-noded tet, it
has a more complex 20 term displacement function that includes all 10 second
order terms, 7 third order terms, and 3 fourth order terms.
When this information is considered together with the other factors
influencing accuracy and efficiency, the "best" element choice becomes
highly problem dependent.
WSZ
CAEA
-----Original Message-----
To: 'xansys@o...'
>From: John Swanson
> With mid-side node elements (10 node tet, 20 node bricks), the
>results should be the same (very close) for the same nodal density.
>The tet mesh will have more nodes because of the nodes in the
>center of the faces and in the center of the brick, and therefore will
>be somewhat more accurate.
> The advantage of fully automatic mesh generation offered by the
>tet elements normally outweighs the additional time the solution
>might take (computers are cheaper than people, and time is always
>critical).
>John.Swanson
>> -----Original Message-----
>> From: Johan Hsu;(W)439-7624;1E09-100 [SMTP:hsujx@o...]
>> Sent: Monday, December 14, 1998 9:32 AM
>> To: xansys@o...
>> Subject: [xansys] Re: FW: Hex & Tet elements
>> From: "Johan Hsu;(W)439-7624;1E09-100"
>> I don't have my book with me right now but I do remember that the Hex
>> elements
>> produce better result than Tet elements only when the edges of the
>> Hex's form at
>> right angles.(4 degree either side?) In the other word, if the
>> element is
>> distorted 3 Tet's produce better result than a single Hex. Correct me
>> if I got
>> it all wrong.
>> J. Hsu
>> > Date: Mon, 14 Dec 1998 10:20:40 +0100
>> > From: Roberto Muccini
>> > To: xansys@o...
>> > Mailing-List: list xansys@o...; contact
>> xansys-owner@o...
>> > Delivered-To: mailing list xansys@o...
>> > List-Unsubscribe:
>> > Mime-Version: 1.0
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>> > Subject: [xansys] Re: FW: Hex & Tet elements
>> > From: Roberto Muccini
>> > Ng Siu Wai, Alex wrote:
>> > > From: "Ng Siu Wai, Alex"
>> > > -----Original Message-----
>> > > From: Binxin Wang [SMTP:wangbinxin@h...]
>> > >
>> > > Sent: Friday, December 11, 1998 10:59 PM
>> > > To: feusers@m...
>> > > Subject: Hex & Tet elements
>> > > Dear all,
>> > > Can any one there provide any reference explaining theoretically
>> why linear
>> > > Hex elements produce better results than Tet elements.
>> > > Thanks in advance.
>> > > Regards.
>> > > Binxin
>> > FE routines calculate results in a fixed number of points for each
>> > elements (Gauss points) then average across the element. The
>> accuracy of
>> > results is function of the number of this points (then the
>> interpolation
>> > function order): e.g. if you have two points you can use a linear
>> > function, if three a quadratic, ecc.
>> > This are only few words about this matter. You can find exhaustive
>> > explanation in every basic FE book.
>> > For example:
>> > Cook et al. "Concepts and applications of finite elemnt analysis",
>> > second edition, John Wiley and Sons, New York 1981
>> > Bathe et al. "Finite element Procedures in Engineering Analysis",
>> > Prentice Hall, Englewood Cliffs 1982
>> > Zienkiewicz et al. "The finite element method", Mc-Graw Hill
>> Company,
>> > London 1977
>> > Hope this helps
>> > Roberto Muccini
>> > Muccini Roberto
>> > Laboratorio di Tecnologia dei Materiali tel.
>> +39-(0)51-6366864550
>> > Istituti Ortopedici Rizzoli fax. +39-(0)51-6366863
>> > via di Barbiano 1/10
>> e-mail:muccini@t...
>> > 40136 Bologna, Italy
>> Johan Hsu, MSME
>> FEA Analytical Engineer
>> SIEMENS Westinghouse Power Corp.
>> Orlando, Florida