Simulation and automation of calculations of buildings (structures) on seismic effects

In many countries there are standards as one-dimensional, console systems for calculations of buildings, which stay in contradiction with the experience of destructive earthquakes. This scientific work offers an explanation for the transfer from one-dimensional to three-dimensional models of different complexity in standards. Discretely-continuous and discrete models of buildings have already been worked out as unified three-dimensional systems with floors deforming in their own plane.

We have considered models of seismic effects, which take into account the effect of the running seismic wave under the ground and the effect of non-uniformity of oscillation field along an extended building or a structure. We pointed out paradoxes in calculations while using three-dimensional models of buildings and “zero-dimensional” (normative) models of soil seismic effects on their grounds. In relation to this problem, we have executed the correction of the formula for determination of seismic forces.

Variational methods of making up the solving equations have been developed for calculation of oscillations of buildings as dynamic systems of large dimension. The structural analysis of buildings, of hydraulic structures, of bridges and of ship hulls has expediently proved to choose own vectors of rigidity matrixes separated out of a three-dimensional object of flat elements as possible displacements. It is the key to “rolling-up” extensive solving equations with thousands of the unknowns and “compressing” the three-dimensional object in one or two directions.

In order to simplify the calculations, we use so-called principle of partial symmetry, connected with mechanisms of deformation of cross- or longitudinal-sections of a three-dimensional construction. The principle can be considered as transformations leaving mathematical objects (tensors) invariant. In mathematical plan the symmetry causes break-up of solving equations into the independent blocks.

In an effort to adjust sequentially solutions, a hierarchical chain of mathematical simulation models of different levels was built, in which own vectors of flat elements are considered as hypotheses of deformation. We have developed program complex “PRIS” to automize calculations of buildings by three-dimensional models. The spectral methods of calculations are generalized for universal three-dimensional models of buildings to use standards of different countries in the developed program complex.