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CALCULATOR MODULE : Elliptical And Semi Elliptical Beam Cross Section ±
Calculate beam cross section properties for elliptical and semi elliptical beams: cross section area, moment of inertia, polar moment of inertia, mass moment of inertia, plastic modulus, section modulus, shape factor, radius of gyration, EI, EA, EAα, unit mass, total mass, unit weight and specific gravity. For hollow ellipse and semi ellipse sections the internal and external sections can be assumed elliptical (the wall thickness is not constant), or the wall thickness can be assumed constant (the mid wall is assumed elliptical but the internal and external surfaces are not elliptical). Refer to the figures for more details. Reference : Roark's Formulas For Stress And Strain, Warren C Young, McGraw Hill Change Module : |
CALCULATOR MODULE : Maths Special Function ±
Calculate special function values. Elliptic integrals are calculated using Carlsons forms. Jacobi elliptic functions are calculated using Landens transformation. The Gamma function is calculated using the Lanczos approximation. Reference : Numerical Recipes, The Art Of Scientific Computing, Press, Teukolsky, Vetterling, Flannery, Cambridge University Press Change Module : |
CALCULATOR MODULE : Maths Elliptic Integral ±
Calculate the complete and incomplete elliptic integrals of the first, second and third kind from the elliptic k modulus. Elliptic integrals are calculated for an ellipse of the form `x^2 + (y / b)^2 = 1 `
`k = √(1 - 1 / b^2) ` where : k = the elliptic k modulus For a circle k = 0. k tends to 1 as b tends to infinity. Use the Result Plot option to plot the integrals versus the k modulus. Reference : Numerical Recipes, The Art Of Scientific Computing, Press, Teukolsky, Vetterling, Flannery, Cambridge University Press Change Module : |
CALCULATOR MODULE : Maths Elliptic Function ±
Calculate the elliptic functions and elliptic amplitude (sn, cn, dn and am). Elliptic functions are calculated for an ellipse of the form `x^2 + (y / b)^2 = 1 `
`k = √(1 - 1 / b^2) ` where : k = the elliptic k modulus For a circle k = 0. k tends to 1 as b tends to infinity. Use the Result Plot option to plot the elliptic functions versus the k modulus. Reference : Numerical Recipes, The Art Of Scientific Computing, Press, Teukolsky, Vetterling, Flannery, Cambridge University Press Change Module : |
CALCULATOR MODULE : Maths Elliptic Functions ±
Calculate maths elliptic functions (sn, cn, and dn). The ellipse is of the form. `x^2 + (y/b)^2 = 1 `
`m = √(1 - 1/b^2) `
`x = (cn(u, m)) / (dn(u, m)) `
`y = (sn(u, m)) / (dn(u, m)) ` where : b = the semi major axis (y axis)
u = the elliptic arc length
m = the elliptic parameter The semi minor axis (x axis) a = 1, and the semi major axis (y axis) b ≥ 1. The elliptic parameter 0 ≤ m ≤ 1. There is an alternative form for m which is used in some methods. `m' = 1 - 1/b^2 `
`m' = m^2 ` Refer to the Keisan special function calculators for check values (https://keisan.casio.com/ : Home => Professional => Special Function => Elliptic Function). The Keisan functions use u and k instead of u and m. Reference : Numerical Calculation of Elliptic Integrals and Elliptic Functions, R. Bulirsch, 1965 Change Module : |
CALCULATOR MODULE : Cnoidal Fifth Order Wave ±
Calculate Cnoidal wave velocity, acceleration and surface profile using Fentons 1999 fifth order wave method. The Cnoidal wave is defined by the elliptic modulus m, the wave trough depth w, and the wave alpha parameter α. The Cnoidal wave model is a truncated series and is only valid within certain ranges. The Cnoidal wave theory is not recommended where the wavelength over water depth ratio (Lod) is less than 8. The recommended wave type is displayed below the calc bar. Note : The cnoidal wave theory uses a truncated infinite series. The truncated series is only valid for conditions where the series converges (m > 0.8). For deep water waves with small m, the series does not converge (use the Stokes wave instead). Check that the convergence is close to or equal to one. The wave period should be measured at zero current velocity to avoid Doppler effects. Reference : J D Fenton, The Cnoidal Theory Of Water Waves, Developments in Offshore Engineering, Gulf, Houston, chapter 2, 1999 Related Modules : |