Computational Mechanics Australia Pty Ltd
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QUAD-SHELL
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
Water Tank Example from the QUAD-SHELL Book
To illustrate the use of the QUAD-SHELL software, consider deformation of a cylindrical water tank under the force of hydrostatic pressure.
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.
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.
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.
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.
The book is available on Amazon as paperback or hardcover.
You can also order the book by contacting Computational Mechanics Australia Pty. Ltd. by e-mail on comecau@ozemail.com.au or comecau1@bigpond.net.au.

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