{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

prob_06_02_01 - Problem 6.2-1 For the element in Fig 6.2-1a...

Info icon This preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
Problem 6.2-1 For the element in Fig. 6.2-1a, let x = [1 ξ η ξη ] [a 1 a 2 a 3 a 4 ] T . (a) Write matrix [A] in the relation [x 1 x 2 x 3 x 4 ] T = [A] [a 1 a 2 a 3 a 4 ] T . (b) By inspection of Eqs. 6.2-3, write [A] -1 in the relation x = [1 ξ η ξη ] [A] -1 [x 1 x 2 x 3 x 4 ] T (c) Check answers to parts (a) and (b) by seeing if [A] [A] -1 = [ I ] Solution: (a) Applying the interpolation equation: x 1 ξ η ξη ( ) a 1 a 2 a 3 a 4 = at each node gives: x 1 x 2 x 3 x 4 A a 1 a 2 a 3 a 4 = A 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 := (b) since a 1 a 2 a 3 a 4 A 1 x 1 x 2 x 3 x 4 = then x 1 ξ η ξη ( ) a 1 a 2 a 3 a 4 = becomes x 1 ξ η ξη ( ) A 1 x 1 x 2 x 3 x 4 = From Eq. 6.2-3 N 1 1 4 1 ξ ( ) 1 η ( ) = 1 4 1 ξ η ξη + ( ) = 1 4 1 ξ η ξη ( ) 1 1 1 1 ( ) T = N 2 1 4 1 ξ + ( ) 1 η ( ) = 1 4 1 ξ + η ξη ( ) = 1 4 1 ξ η ξη ( ) 1 1 1 1 ( ) T = N 3 1 4 1 ξ + ( ) 1 η + ( ) = 1 4 1 ξ + η + ξη + ( )
Image of page 1
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern