of the static analysis of the arch dam Karakaya in Turkey
by Dr. sc. techn. ETH Rudolf Trinkner

2.1 The Dam Body


To treat the double-curved shape of the Karakaya dam as a collection of flat elements, it was divided into 521 triangle-shaped finite elements in a way that angles between adjacent ele-ments are lower than 5 degrees (10 degrees being generally acceptable). Hybrid elements were used to take shear deformations in thick shells (like Karakaya) into account. These hybrid elements are described as follows:

  • The assumptions for the internal stresses meet the homogeneous differential equations of the balance. However, this leads to discontinuities along the element edges (The mean is taken at the nodes).
  • The functions for displaced edges of elements were chosen so that the kinematic compati-bility along the edges is guaranteed.
  • The matrices for stiffness, stress and load were formed in application of the principle of complementary energy so that the hybrid stress model leads to the deformation method matrix.
  • All element integrations were executed numerically. This allows the use of randomly shaped triangular elements.

Results lie between the solution of a constantly too stiff behaving compatible deformation model with equivalent edge-shifting and the solution of a constantly too soft behaving pure balance model with the same stress approaches. Thus a coarse element mesh will lead to exact results as well.