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--- wikifemfuchde2020:crosssectionalpropsthroughfem [2020/04/23 19:15] – [Thin walled profile in bending] ebertocchi
+++ wikifemfuchde2020:crosssectionalpropsthroughfem [2020/04/23 19:16] (versione attuale) – [Thin walled profile in bending] ebertocchi
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+===== Thin walled profile in torsion =====
+Please note that the techniques employed rely on the //monoclinic// nature of the material with respect to the cross-sectional plane, i.e. such a plane is required to be a symmetry plane for the material.
+Open thin-walled rectangular cross section profile (a longitudinal cut is performed at the lateral wall center line, whose kerf (width) is negligible), 80x40mm at the midsurface,  6mm wall thickness.
+Element size of ~10mm.
+The severed lateral wall may be easily deactivated to reproduce the simplified ladder-frame chassis cross section.
+{{:wikifemfuchde2018:analisi_sezione_a_torsione.png?nolink|}}
+{{:wikifemfuchde2018:analisi_sezione_a_torsione.pdf |sorgente ipe}}
+At the A cross section, a skew-symmetry material continuity constraint is applied.
+The kinematic constraint at the B point (sphere in cylinder joint) is a positioning constraint, along with the $w_A=0$ axial constraint in A.
+A twist per unit length equaling 0.001 radiant/mm is imposed to the profile, i.e. a $\psi_B=0.001 \cdot l$ rotation is imposed at each end, where $l$ is the  $z$ axial coordinate of the endpoints, being z=0 at the skew-symmetry plane.
+The reaction moment associated with the constraint will determine the applied torque $T$.
+----
+{{ :wikifemfuchde2020:profile_in_torsion_a2020_v000.mfd | profile geometry alone}}
+{{ :wikifemfuchde2020:profile_in_torsion_a2020_v005.mfd | model at the end of the 2020-04-02 lesson}}
+{{ :wikifemfuchde2020:profile_in_torsion_a2020_v008.mfd | model at the end of the 2020-04-06 lesson}}
+{{ :wikifemfuchde2020:profile_in_torsion_a2020_v010.mfd |}}
+{{ :wikifemfuchde2020:profile_in_torsion_a2020_v011.mfd | model at the end of the 2020-04-09 lesson}}
+{{ :wikifemfuchde2020:profile_in_torsion_a2020_v012.mfd | model at the end of the 2020-04-12 lesson}}, and
+{{ :wikifemfuchde2020:profile_in_torsion_a2020_v012m.mfd | the same model, with increasingly refined in-cross-section discretizations}}. Please observe (try it!) that no change in results is obtained by further splitting the elements in the axial directions; such a result is related to the fact that stresses are observed to be constant along the same direction.
+{{ :wikifemfuchde2020:torsional_stiffness_evaluation_ffcd2020_v000.xls | LibreOffice/MSExcel spreadsheet for the collection and the normalization of the results}}, to be filled as homework.
+At the end of the 2020-04-16 lesson:
+{{ :wikifemfuchde2020:profile_in_torsion_a2020_v013.mfd |otw model}},
+{{ :wikifemfuchde2020:profile_in_torsion_a2020_v013c.mfd |ctw model}}.
+spreadsheet with increased profile length
+{{ :wikifemfuchde2020:torsional_stiffness_evaluation_ffcd2020_v001.xls |}}, and the associated
+{{ :wikifemfuchde2020:profile_in_torsion_a2020_v014.mfd |otw model}}
+and
+{{ :wikifemfuchde2020:profile_in_torsion_a2020_v014c.mfd |ctw model}}.
+===== Thin walled profile subject to pure shear =====
+Various incremental steps in the definition of the shear loadcase
+{{ :wikifemfuchde2020:profile_in_torsion_a2020_v015.mfd |v015}}
+{{ :wikifemfuchde2020:profile_in_torsion_a2020_v016.mfd |v016}}
+{{ :wikifemfuchde2020:profile_in_torsion_a2020_v017.mfd |v017}}
+{{ :wikifemfuchde2020:profile_in_torsion_a2020_v018.mfd |v018}}, and the
+{{ :wikifemfuchde2020:torsional_stiffness_evaluation_ffcd2020_v001.xls |updated spreadsheet}}.
+{{ :wikifemfuchde2020:profile_in_torsion_a2020_v018.mfd |v018}} is the final model for the response evaluation of the cross section to skew-symmetric internal action components ($M_t$,$Q_x$,$Q_y$).
+Please note that, for the application of the presented procedure, the global (O,x) (O,y) axes **must** coincide with the principal axes of (elastic) inertia for the cross section.
+===== Thin walled profile in bending =====
+For reference/review purposes: {{ :wikifemfuchde2020:last_year_notes_on_bending_and_shear.pdf |}}.
+Please read attentively the first paragraph devoted to axial load and bending; if something is not clear, please ask the professor.
+Such a treatise should constitute just a slight extension of what you already encountered in previous //Strength of Materials// courses.
+{{ :wikifemfuchde2020:profile_in_bending_a2020_v001.mfd |}}
+{{ :wikifemfuchde2020:profile_in_bending_a2020_v002.mfd |}}
+{{ :wikifemfuchde2020:profile_in_bending_a2020_v003.mfd |}}
+{{ :wikifemfuchde2020:symmprops.ods |}}
+{{ :wikifemfuchde2020:symmprops_v003.ods |}}
+Solution:
+{{ :wikifemfuchde2020:profile_in_bending_a2020_v003a.mfd |FE model with unit curvature loadcases}},
+{{ :wikifemfuchde2020:symmprops_v003a.ods |Spreadsheet with the collected results}},
+{{ :wikifemfuchde2020:profile_in_bending_a2020_v003a.mfd |FE model re-oriented}} s.t. the global (O,x) (O,y) axes coincide with the principal axes of (elastic) inertia for the cross section, in order to proceed with the pure shear analysis.
+Auxiliary {{ :wikifemfuchde2020:eig2x2.wxmx |maxima worksheet}} for literally solving the 2x2 eigenvalue problem.