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A new book and software for modeling of shells based on the Kirchhoff-Love theory
Available with source codes and intended for scientific and engineering research
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Water Tank Example from the QUAD-SHELL Book
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To illustrate the use of the QUAD-SHELL
software, consider deformation of a cylindrical water tank under the force of
hydrostatic pressure.
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The tank is fully filled with water. The hydrostatic pressure acting on the walls
at a particular level is a linear function with respect to the vertical coordinate.
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Since the water tank has a cylindrical shape, the geometrical parameters of its surface are readily evaluated: the Lame coefficients equal zero and R; the main curvatures equal zero and 1/R, respectively.
The water tank is made of a material with the following properties: the Young modulus is
14 GPa, the Poisson ratio is zero.
To illustate that the QUAD-SHELL algorithm for
constructing the lines of principal curvature imposes no constraints on the finite elements shapes, we shall consider a rather irregular finite element mesh.
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The bottom of the tank is built-in. Since it cannot deflect freely under loading,
there occur statically indeterminate shear forces and bending moments.
Due to the water pressure increasing from top to bottom, the material of the cylinder
is expected to experience the biggest internal stresses close to the bottom .
This justifies the creation of a fine mesh on the lower part of the model.
An exact analytical solution is given in the book "Osnovy Rascheta Uprugikh Obolochek"
by N. V. Kolkunov (in Russian). The analytical formulae express the radial displacement,
the circumferential tensile force and the bending moment as functions of
the vertical coordinate z.
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Comparing the diagrams of the cicumferential tensile force and the bending moment
for the analytical and numerical solutions, we can observe that the diagrams of
circumferential tensile forces are practically identical, whereas the values of the
maximum analytical and numerical bending moments slightly differ, but the relative
error is less that 5%. Futher error reduction can be achieved by using a more refined
mesh at the botton of the water tank.
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You can also order the book by contacting Computational Mechanics Australia Pty. Ltd. by e-mail on
comecau@ozemail.com.au or
comecauinfo@gmail.com.
To learn more about full range of our products please follow this
link.
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