Abstract: In order to reduce numerical computations in the
nonlinear dynamic analysis of seismically base-isolated structures, a
Mixed Explicit-Implicit time integration Method (MEIM) has been
proposed. Adopting the explicit conditionally stable central
difference method to compute the nonlinear response of the base
isolation system, and the implicit unconditionally stable Newmark’s
constant average acceleration method to determine the superstructure
linear response, the proposed MEIM, which is conditionally stable
due to the use of the central difference method, allows to avoid the
iterative procedure generally required by conventional monolithic
solution approaches within each time step of the analysis. The main
aim of this paper is to investigate the stability and computational
efficiency of the MEIM when employed to perform the nonlinear
time history analysis of base-isolated structures with sliding bearings.
Indeed, in this case, the critical time step could become smaller than
the one used to define accurately the earthquake excitation due to the
very high initial stiffness values of such devices. The numerical
results obtained from nonlinear dynamic analyses of a base-isolated
structure with a friction pendulum bearing system, performed by
using the proposed MEIM, are compared to those obtained adopting a
conventional monolithic solution approach, i.e. the implicit
unconditionally stable Newmark’s constant acceleration method
employed in conjunction with the iterative pseudo-force procedure.
According to the numerical results, in the presented numerical
application, the MEIM does not have stability problems being the
critical time step larger than the ground acceleration one despite of
the high initial stiffness of the friction pendulum bearings. In
addition, compared to the conventional monolithic solution approach,
the proposed algorithm preserves its computational efficiency even
when it is adopted to perform the nonlinear dynamic analysis using a
smaller time step.
Abstract: The solution of the nonlinear dynamic equilibrium equations of base-isolated structures adopting a conventional monolithic solution approach, i.e. an implicit single-step time integration method employed with an iteration procedure, and the use of existing nonlinear analytical models, such as differential equation models, to simulate the dynamic behavior of seismic isolators can require a significant computational effort. In order to reduce numerical computations, a partitioned solution method and a one dimensional nonlinear analytical model are presented in this paper. A partitioned solution approach can be easily applied to base-isolated structures in which the base isolation system is much more flexible than the superstructure. Thus, in this work, the explicit conditionally stable central difference method is used to evaluate the base isolation system nonlinear response and the implicit unconditionally stable Newmark’s constant average acceleration method is adopted to predict the superstructure linear response with the benefit in avoiding iterations in each time step of a nonlinear dynamic analysis. The proposed mathematical model is able to simulate the dynamic behavior of seismic isolators without requiring the solution of a nonlinear differential equation, as in the case of widely used differential equation model. The proposed mixed explicit-implicit time integration method and nonlinear exponential model are adopted to analyze a three dimensional seismically isolated structure with a lead rubber bearing system subjected to earthquake excitation. The numerical results show the good accuracy and the significant computational efficiency of the proposed solution approach and analytical model compared to the conventional solution method and mathematical model adopted in this work. Furthermore, the low stiffness value of the base isolation system with lead rubber bearings allows to have a critical time step considerably larger than the imposed ground acceleration time step, thus avoiding stability problems in the proposed mixed method.
Abstract: This paper focuses on a technique for identifying the geological boundary of the ground strata in front of a tunnel excavation site using the first order adjoint method based on the optimal control theory. The geological boundary is defined as the boundary which is different layers of elastic modulus. At tunnel excavations, it is important to presume the ground situation ahead of the cutting face beforehand. Excavating into weak strata or fault fracture zones may cause extension of the construction work and human suffering. A theory for determining the geological boundary of the ground in a numerical manner is investigated, employing excavating blasts and its vibration waves as the observation references. According to the optimal control theory, the performance function described by the square sum of the residuals between computed and observed velocities is minimized. The boundary layer is determined by minimizing the performance function. The elastic analysis governed by the Navier equation is carried out, assuming the ground as an elastic body with linear viscous damping. To identify the boundary, the gradient of the performance function with respect to the geological boundary can be calculated using the adjoint equation. The weighed gradient method is effectively applied to the minimization algorithm. To solve the governing and adjoint equations, the Galerkin finite element method and the average acceleration method are employed for the spatial and temporal discretizations, respectively. Based on the method presented in this paper, the different boundary of three strata can be identified. For the numerical studies, the Suemune tunnel excavation site is employed. At first, the blasting force is identified in order to perform the accuracy improvement of analysis. We identify the geological boundary after the estimation of blasting force. With this identification procedure, the numerical analysis results which almost correspond with the observation data were provided.
Abstract: This paper deals with a numerical analysis of the
transient response of composite beams with strain rate dependent
mechanical properties by use of a finite difference method. The
equations of motion based on Timoshenko beam theory are derived.
The geometric nonlinearity effects are taken into account with von
Kármán large deflection theory. The finite difference method in
conjunction with Newmark average acceleration method is applied to
solve the differential equations. A modified progressive damage
model which accounts for strain rate effects is developed based on
the material property degradation rules and modified Hashin-type
failure criteria and added to the finite difference model. The
components of the model are implemented into a computer code in
Mathematica 6. Glass/epoxy laminated composite beams with
constant and strain rate dependent mechanical properties under
dynamic load are analyzed. Effects of strain rate on dynamic
response of the beam for various stacking sequences, load and
boundary conditions are investigated.