Module platepy.analyticPlateSolutions

Provide analytic plate bending solutions. Solutions stem from Timoshenko's book: "Plates and Shells" (1959).

Functions

def AnalyticPlateSolutions(pOpts, lOpts, sOpts, inPos)

Compute the analytical solution of a plate problem according to Timoshenko's book "Theory of plates and shells" (1959).

INPUT
  • pOpts : object with following attributes
    • pOpts.shape = "rectangular" or "circular".
    • pOpts.depth = "thick" or "thin".
    • pOpts.support = "simplySupported" or "clamped".
    • pOpts.geometry = for rectangles: tuple with (a,b) dimensions, for circles: radius r.
    • pOpts.material = material object.
  • lOpts : object with following attributes
    • lOpts.type = "concentrated" or "distributed"
    • lOpts.position = if the load is concentrated, tuple with (x,y) coordinates.
    • lOpts.magnitude = magnitude of vertical force.
  • sOpts : solution options
    • sOpts.nTerms = Integer, number of terms in the Taylor expansion.
  • inPos : Numpy array with shape (n, 2) containing the positions at which output quantities are requested.
RETURN
  • quantities = boolean list (of size 8) of calculated and therefore returned outputs (possible: Wz, Rx, Ry, Mx, Mx, Mxy, Vx, Vy).
  • values = Numpy array of size (length(inPos),nReturnedQuantities ) containing quantities calculated at inPos.
  • outPos = Numpy array of size (length(inPos), 2, nReturnedQuantities) containing positions where output quantities are calculated.

Classes

class LOpts

Load options.

ATTRIBUTES
  • lOpts.type = "concentrated" or "distributed"
  • lOpts.position = if the load is concentrated, tuple with (x,y) coordinates.
  • lOpts.magnitude = magnitude of vertical force.
class Material (E, nu, h)

Stores material properties for the pOpts class.

INPUT
  • E: Young's modulus.
  • nu: Poisson's ratio.
  • h: Plate's thickness.
ATTRIBUTES
  • myLambda: For analytical models containing beam stiffeners, ratio between beam and plate stiffness (EI/aD).
class POpts

Plate options.

ATTRIBUTES
  • pOpts.shape = "rectangular" or "circular".
  • pOpts.depth = "thick" or "thin".
  • pOpts.support = "simplySupported" or "clamped".
  • pOpts.geometry = for rectangles: tuple with (a,b) dimensions, for circles: radius r.
  • pOpts.material = material object.
class SOpts (nTerms=20)

Solution options.

ATTRIBUTES

sOpts.nTerms = 20 = number of terms of the Taylor's expansions, by default 20 (usually is enough)."