Continuation methods: proceedings of a symposium at the by H. Wacker

By H. Wacker

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Additional resources for Continuation methods: proceedings of a symposium at the University of Linz, Austria, October 3-4, 1977

Example text

For practical engineering problems, one usually does not have to pursue the exact solution, which in most cases are usually unobtainable, because we now have a choice to quite conveniently obtain a good approximation using Hamilton’s principle, by assuming the likely form, pattern or shape of the solutions. Hamilton’s principle thus provides the foundation for the finite element methods. Furthermore, the simplicity of Hamilton’s principle (or any other energy principle) manifests itself in the use of scalar energy quantities.

This shows that the partitions of unity of the shape functions in the element allows a constant field or rigid body movement to be reproduced. Note that Eq. 41) does not require 0 ≤ Ni (x) ≤ 1. Property 5. e. 44) i=1 where xi is the nodal values of the linear field. This can be proven easily from the reproduction feature of the shape function in exactly the same manner for proving Property 4. Let u(x) = x, we should have de = x1 , x2 , . . 45) Substituting the above equation into Eq. 24), we obtain uh (x) = x = nd Ni (x)xi 1 which is Eq.

Therefore in this book, shell structures will be modelled by combining plate elements and 2D solid elements. 2. The surface of the solid is further divided into two types of surfaces: a surface on which the external forces are prescribed is denoted SF ; and surface on which the displacements are prescribed is denoted Sd . The solid can also be loaded by body force f b and surface force fs in any distributed fashion in the volume of the solid. 3. On each surface, there will be the normal stress component, and two components of shearing stress.

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