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Chapter 8 – Linear Strain Triangle (Overview)

Chapter 8 – Linear Strain Triangle (Overview). Compare formulation of CST and LST Comparison of element performance. Comparison of CST and LST Formulations. CST: Three nodes per element 6 DOF per element. LST: 6 nodes per element 12 DOF per element. Displacement Interpolation.

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Chapter 8 – Linear Strain Triangle (Overview)

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  1. Chapter 8 – Linear Strain Triangle(Overview) • Compare formulation of CST and LST • Comparison of element performance

  2. Comparison of CST and LST Formulations • CST: • Three nodes per element • 6 DOF per element • LST: • 6 nodes per element • 12 DOF per element

  3. Displacement Interpolation CST: LST:

  4. Strains within each element Recall: CST: LST:  ~ constant => Constant Strain Triangle (CST)  ~ at most linear in x & y => Linear Strain Triangle (LST)

  5. 6x6 6x3 3x6 3x3 12x12 12x3 3x3 3x12 Element Stiffness Matrix CST: LST: Since Bij terms depend on x & y, numerical integration is required (Chap. 10)

  6. CST vs. LST – Performance Comparison Consider the following plane stress analysis of a cantilever beam “4 x 16” mesh

  7. CST vs. LST – Performance Comparison(cont.) Test Cases:

  8. CST vs. LST – Performance Comparison(cont.)

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