CVEN4304-TutorialSet5-IsoparametricElements

CVEN4304-TutorialSet5-IsoparametricElements - THE...

This preview shows page 1 - 2 out of 2 pages.

THE UNIVERSITY OF NEW SOUTH WALES SCHOOL OF CIVIL AND ENVIRONMENTAL ENGINEERING CVEN 4304: STRUCTURAL ANALYSIS AND FINITE ELEMENTS CVEN9820 COMPUTATIONAL STRUCTURAL MECHANICS Tutorial Set 5: Isoparametric Element Determine the 3 by 3 stiffness matrix if nodes of the element in figure are uniformly spaced. Let A and E be constant and perform integrations explicitly. Figure 1 Omit the internal node in Figure 1, so that the element becomes a bar with end nodes only. Using natural coordinates , derive the 2 by 2 stiffness matrix of a uniform element. In Figure 1, let 4 / 2 3 L x x and 4 / 3 1 2 L x x . If only node 3 has axial displacement ( 0 2 1 u u , 0 3 u ), what is the strain x at each node. Evaluate [J] and J for each of the four elements shown. Also determine the ratio of element area to the area of a square two units on a side. How is this ratio related to J, and why?
Image of page 1

Subscribe to view the full document.

Image of page 2

Unformatted text preview: area to the area of a square two units on a side. How is this ratio related to J, and why? Figure 2 Repeat Question 1, but use two-point Gauss quadrature rather than explicit integration. A quadrilateral element is shown in the figure with the coordinates in millimeters. Let E =210 GPa and v =0.25 and assume plane stress condition. Use a spreadsheet (for example, MS Excel), MATLAB, MAPLE or MATHEMATICA 1. To evaluate the element stiffness matrix using 1-by-1 Gaussian quadrature. 2. To evaluate the element stiffness matrix using 2-by-2 Gaussian quadrature. 3. To determine the stresses at the local coordinates (0,0) when the displacements are given as u 1 =0, v 1 =0; u 2 =0.01mm, v 2 =0.005mm; u 3 =0.015mm, v 3 =0.02mm; u 4 =0, v 4 =0. Figure 3...
View Full Document

  • Three '10
  • HneryYip
  • Numerical Analysis, Ratio, Chemical element, Finite element method in structural mechanics, SCHOOL OF CIVIL, COMPUTATIONAL STRUCTURAL MECHANICS

{[ snackBarMessage ]}

Get FREE access by uploading your study materials

Upload your study materials now and get free access to over 25 million documents.

Upload now for FREE access Or pay now for instant access
Christopher Reinemann
"Before using Course Hero my grade was at 78%. By the end of the semester my grade was at 90%. I could not have done it without all the class material I found."
— Christopher R., University of Rhode Island '15, Course Hero Intern

Ask a question for free

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