feat(fem): plastic section modulus of a circular section#436
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Add beam::circular_plastic_section_modulus(diameter), the plastic section modulus of a solid round section: Z = d^3 / 6 (m^3) the section property for fully-plastic limit bending of a shaft (M_plastic = sigma_y * Z) -- the circular companion to rectangular_plastic_section_modulus (#426). For a solid circle the shape factor is Z/S = 16/(3*pi) ~= 1.698 (Z = d^3/6 vs the elastic S = pi*d^3/32). Guard mirrors circular_second_moment_of_area. Analytic test circular_plastic_section_modulus_is_d3_over_6: (a) worked d=0.1 -> Z = 1.6667e-4 m^3; (b) threads elastic_section_modulus + circular_second_moment_of_area (#419) (non-tautological): Z = (16/3pi)*S and the shape factor Z/S = 16/(3pi); (c) cubic in diameter; (d) 0-sentinel guards for non-positive d and non-finite input. Re-exported from lib.rs alphabetically in the beam block. valenx-fem 263 lib tests (was 262), cargo clippy --all-targets -D warnings clean.
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What
Adds
beam::circular_plastic_section_modulus(diameter)— the plastic section modulus of a solid round section:Why
The section property for fully-plastic limit bending of a shaft (
M_plastic = sigma_y * Z) — the circular companion torectangular_plastic_section_modulus(#426). For a solid circle the shape factor isZ/S = 16/(3*pi) ~= 1.698(Z = d^3/6vs the elasticS = pi*d^3/32). Guard mirrorscircular_second_moment_of_area. This completes the{rectangular, circular} x {elastic-S, plastic-Z}section-modulus grid.Test
circular_plastic_section_modulus_is_d3_over_6:d=0.1 -> Z = 1.6667e-4 m^3;elastic_section_modulus+circular_second_moment_of_area(feat(cfd): vorticity standard deviation (variance identity) #419) (non-tautological) —Z = (16/3pi)*Sand the shape factorZ/S = 16/(3pi);dand non-finite input.Re-exported from
lib.rsalphabetically in the beam block.valenx-fem263 lib tests (was 262);cargo clippy -p valenx-fem --all-targets -- -D warningsclean. Research-grade plastic/limit-analysis section property.