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torsion of non circular cross sections
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Torsion of Non-Circular Prismatic Bars: Finite Element Modeling and AnalysisPertinent reading: Section 11.5 in textbook
V. N. Kaliakin
Idealized Problem
V. N. Kaliakin
Torsion of a Slot Cross-SectionSee Figure 11.14 on p. 432 in textbook.
V. N. Kaliakin
Torsion of a Hollow Slot Cross-SectionG = 1.154e+07 psiQ = 4.433e-04 rad/in
V. N. Kaliakin
Torsion of a Hollow Slot Cross-SectionSolution Domain & its BoundaryWGGGG
V. N. Kaliakin
Torsion of a Hollow Slot Cross-SectionNodal SpecificationsWF = 0F = 0F = 0F = 0F = 0
V. N. Kaliakin
Torsion of a Hollow Slot Cross-SectionCoarsest MeshWill yield a trivial solution!F = 0F = 0F = 0F = 0
V. N. Kaliakin
Torsion of a Hollow Slot Cross-SectionFiner MeshThe key is to also provide nodes not along the boundary!
V. N. Kaliakin
Taking Advantage of Symmetry in Finite Element AnalysesIf a specific problem has one or more lines (axes) of symmetry, the resulting FE analysis can be simplified.This results in fewer elements being used in the solution.Consequently, the computational effort is reduced.
V. N. Kaliakin
Taking Advantage of Symmetry in Finite Element AnalysesTo qualify for conditions of symmetry, the following must be shown to be symmetric with respect to a given axis:
Geometry of the solution domain Material constitution and distribution Applied loading Nodal specifications (boundary conditions)
V. N. Kaliakin
Torsion of a Hollow Slot Cross-SectionSymmetry ConsiderationsWGWe thus only need to analyze one-quarter of W!
V. N. Kaliakin
Torsion of a Hollow Slot Cross-SectionSolution Domain & its BoundaryWGGGSymmetry boundarySymmetry boundaryAlong symmetry boundariesxy
V. N. Kaliakin
First mesh(36 elements)
V. N. Kaliakin
V. N. Kaliakin
Second mesh(144 elements)
V. N. Kaliakin
V. N. Kaliakin
Third mesh(576 elements)
V. N. Kaliakin
V. N. Kaliakin
Torsion of a Filled Slot Cross-SectionG1 = 12.0e+06 psiQ = 4.0e-04 rad/inG2 = 6.0e+06 psi
V. N. Kaliakin
Torsion of a Filled Slot Cross-SectionSolution Domain & its BoundaryWGGG
V. N. Kaliakin
First mesh(20 elements)
V. N. Kaliakin
V. N. Kaliakin
Second mesh(80 elements)
V. N. Kaliakin
V. N. Kaliakin
Torsion of a Semi-Circular Cross-Sectionxyr = 2.0 cm
V. N. Kaliakin
Torsion of a Semi-Circular Cross-SectionSolution Domain & its BoundaryxyWGG
V. N. Kaliakin
First mesh(4 elements/side)
V. N. Kaliakin
V. N. Kaliakin
Second mesh(8 elements/side)
V. N. Kaliakin
V. N. Kaliakin
Third mesh(16 elements/side)
V. N. Kaliakin
V. N. Kaliakin