A Fast Non-Linear, Finite Element Solver for Earthquake Response of Buildings
Thesis DisciplineMechanical Engineering
Degree GrantorUniversity of Canterbury
Degree NameMaster of Engineering
Design of buildings in earthquake regions requires that the building is made to withstand certain large earthquake magnitudes with a degree of permanent, but energy absorbing, damage. To accurately determine the behaviour of the building while damage occurs, a nonlinear analysis must be used as these effects are non-linear. These computations are often very slow as the building’s response must be calculated many times a second.
This thesis seeks to find a faster alternative to the Newmark-β and similar numerical integration schemes commonly used in non-linear seismic structural analysis. Faster computation would enable rapid simulation thus speeding up the design process. It would also allow large Monte Carlo analyses to be done to improve research analysis and allow designers to better account for variability in materials, construction, soil site and other factors that can significantly affect response.
For the purposes of this investigation simple two node finite elements were used. The nonlinear component consists of the well-accepted Ramberg-Osgood hysteresis model. The alternative approach used in this thesis is to solve non-linear first order differential equations using a Runge-Kutta based solution. This approach, with added new computational methods, should be more efficient than directly solving the second order equation of motion with Newmark-β.
Different test cases were run to establish performance differences in a variety of potential user cases. These cases involved testing different models against both real earthquake data and synthetic input accelerations. In all test cases, the Newmark-β solution yielded the same results as the new solution, as long as a small enough time step was used. When a small time step was used and the results agreed, the new solution was much faster than the Newmark-β solution.
In particular, the new numerical solution approach was significantly faster than Newmark-β when the accuracy demanded was 1% or less. As the tolerance was tightened the advantage of the new solution increased exponentially. From this project a set of MATLAB scripts has been created that will reproduce the results given and can also be used to analyse other building models. The overall approach used is also entirely generalisable.