Abstract: Dynamic analysis of composite doubly curved panels with variable thickness subjected to different pulse types using Generalized Differential Quadrature method (GDQ) is presented in this study. Panels with variable thickness are used in the construction of aerospace and marine industry. Giving variable thickness to panels can allow the designer to get optimum structural efficiency. For this reason, estimating the response of variable thickness panels is very important to design more reliable structures under dynamic loads. Dynamic equations for composite panels with variable thickness are obtained using virtual work principle. Partial derivatives in the equation of motion are expressed with GDQ and Newmark average acceleration scheme is used for temporal discretization. Several examples are used to highlight the effectiveness of the proposed method. Results are compared with finite element method. Effects of taper ratios, boundary conditions and loading type on the response of composite panel are investigated.
Abstract: Finding the linear and nonlinear responses of a typical single-degree-of-freedom system (SDOF) is always being regarded as a time-consuming process. This study attempts to provide modifications in the renowned Newmark method in order to make it more time efficient than it used to be and make it more accurate by modifying the system in its own non-linear state. The efficacy of the presented method is demonstrated by assigning three base excitations such as Tabas 1978, El Centro 1940, and MEXICO CITY/SCT 1985 earthquakes to a SDOF system, that is, SDOF, to compute the strength reduction factor, yield pseudo acceleration, and ductility factor.
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: Numerical simulations of vortex-induced vibration of a three-dimensional flexible tube under uniform turbulent flow are calculated when Reynolds number is 1.35×104. In order to achieve the vortex-induced vibration, the three-dimensional unsteady, viscous, incompressible Navier-Stokes equation and LES turbulence model are solved with the finite volume approach, the tube is discretized according to the finite element theory, and its dynamic equilibrium equations are solved by the Newmark method. The fluid-tube interaction is realized by utilizing the diffusion-based smooth dynamic mesh method. Considering the vortex-induced vibration system, the variety trends of lift coefficient, drag coefficient, displacement, vertex shedding frequency, phase difference angle of tube are analyzed under different frequency ratios. The nonlinear phenomena of locked-in, phase-switch are captured successfully. Meanwhile, the limit cycle and bifurcation of lift coefficient and displacement are analyzed by using trajectory, phase portrait, and Poincaré sections. The results reveal that: when drag coefficient reaches its minimum value, the transverse amplitude reaches its maximum, and the “lock-in” begins simultaneously. In the range of lock-in, amplitude decreases gradually with increasing of frequency ratio. When lift coefficient reaches its minimum value, the phase difference undergoes a suddenly change from the “out-of-phase” to the “in-phase” mode.
Abstract: In this paper, a numerical algorithm using a coupled Galerkin-Differential Quadrature (DQ) method is proposed for the solution of dam-reservoir interaction problem. The governing differential equation of motion of the dam structure is discretized by the Galerkin method and the DQM is used to discretize the fluid domain. The resulting systems of ordinary differential equations are then solved by the Newmark time integration scheme. The mixed scheme combines the simplicity of the Galerkin method and high accuracy and efficiency of the DQ method. Its accuracy and efficiency are demonstrated by comparing the calculated results with those of the existing literature. It is shown that highly accurate results can be obtained using a small number of Galerkin terms and DQM sampling points. The technique presented in this investigation is general and can be used to solve various fluid-structure interaction problems.
Abstract: The tension leg platform (TLP) is one of the compliant structures which are generally used for deep water oil exploration. With respect to the horizontal degrees of freedom, it behaves like a floating structure moored by vertical tethers which are pretension due to the excess buoyancy of the platform, whereas with respect to the vertical degrees of freedom, it is stiff and resembles a fixed structure and is not allowed to float freely. In the current study, a numerical study for square TLP using modified Morison equation was carried out in the time domain with water particle kinematics using Airy’s linear wave theory to investigate the effect of changing the tether tension force on the stiffness matrix of TLP's, the dynamic behavior of TLP's; and on the fatigue stresses in the cables. The effect was investigated for different parameters of the hydrodynamic forces such as wave periods, and wave heights. The numerical study takes into consideration the effect of coupling between various degrees of freedom. The stiffness of the TLP was derived from a combination of hydrostatic restoring forces and restoring forces due to cables. Nonlinear equation was solved using Newmark’s beta integration method. Only uni-directional waves in the surge direction was considered in the analysis. It was found that for short wave periods (i.e. 10 sec.), the surge response consisted of small amplitude oscillations about a displaced position that is significantly dependent on tether tension force, wave height; whereas for longer wave periods, the surge response showed high amplitude oscillations that is significantly dependent on wave height, and that special attention should be given to tethers fatigue because of their high tensile static and dynamic stress.
Abstract: The tension leg platform (TLP) is a vertically moored structure with excess buoyancy. The TLP is regarded as moored structure in horizontal plan, while inherit stiffness of fixed platform in vertical plane. In this paper, a numerical study using modified Morison equation was carried out in the time domain to investigate the influence of nonlinearities due to hydrodynamic forces and the coupling effect between surge, sway, heave, roll, pitch and yaw degrees of freedom on the dynamic behavior of TLP's. The stiffness of the TLP was derived from a combination of hydrostatic restoring forces and restoring forces due to cables and the nonlinear equations of motion were solved utilizing Newmark’s beta integration scheme. The effect of tethers length and wave characteristics such as wave period and wave height on the response of TLP's was evaluated.
Only uni-directional waves in the surge direction was considered in the analysis. It was found that for short wave periods (i.e. 10 sec.), the surge response consisted of small amplitude oscillations about a displaced position that is significantly dependent on tether length, wave height; whereas for longer wave periods, the surge response showed high amplitude oscillations about that is significantly dependent on tether length.
Abstract: The effect of different combinations of response
feedback on the performance of active control system on nonlinear
frames has been studied in this paper. To this end different feedback
combinations including displacement, velocity, acceleration and full
response feedback have been utilized in controlling the response of
an eight story bilinear hysteretic frame which has been subjected to a
white noise excitation and controlled by eight actuators which could
fully control the frame. For active control of nonlinear frame
Newmark nonlinear instantaneous optimal control algorithm has been
used which a diagonal matrix has been selected for weighting
matrices in performance index. For optimal design of active control
system while the objective has been to reduce the maximum drift to
below the yielding level, Distributed Genetic Algorithm (DGA) has
been used to determine the proper set of weighting matrices. The
criteria to assess the effect of each combination of response feedback
have been the minimum required control force to reduce the
maximum drift to below the yielding drift. The results of numerical
simulation show that the performance of active control system is
dependent on the type of response feedback where the velocity
feedback is more effective in designing optimal control system in
comparison with displacement and acceleration feedback. Also using
full feedback of response in controller design leads to minimum
control force amongst other combinations. Also the distributed
genetic algorithm shows acceptable convergence speed in solving the
optimization problem of designing active control systems.
Abstract: In general dynamic analyses, lower mode response is
of interest, however the higher modes of spatially discretized
equations generally do not represent the real behavior and not affects
to global response much. Some implicit algorithms, therefore, are
introduced to filter out the high-frequency modes using intended
numerical error. The objective of this study is to introduce the
P-method and PC α-method to compare that with dissipation method
and Newmark method through the stability analysis and numerical
example. PC α-method gives more accuracy than other methods
because it based on the α-method inherits the superior properties of the
implicit α-method. In finite element analysis, the PC α-method is more
useful than other methods because it is the explicit scheme and it
achieves the second order accuracy and numerical damping
simultaneously.
Abstract: In this study, aeroelastic response and performance
analyses have been conducted for a 5MW-Class composite wind
turbine blade model. Advanced coupled numerical method based on
computational fluid dynamics (CFD) and computational flexible
multi-body dynamics (CFMBD) has been developed in order to
investigate aeroelastic responses and performance characteristics of
the rotating composite blade. Reynolds-Averaged Navier-Stokes
(RANS) equations with k-ω SST turbulence model were solved for
unsteady flow problems on the rotating turbine blade model. Also,
structural analyses considering rotating effect have been conducted
using the general nonlinear finite element method. A fully implicit
time marching scheme based on the Newmark direct integration
method is applied to solve the coupled aeroelastic governing equations
of the 3D turbine blade for fluid-structure interaction (FSI) problems.
Detailed dynamic responses and instantaneous velocity contour on the
blade surfaces which considering flow-separation effects were
presented to show the multi-physical phenomenon of the huge rotating
wind- turbine blade model.
Abstract: The mechanical behavior of porous media is governed by the interaction between its solid skeleton and the fluid existing inside its pores. The interaction occurs through the interface of gains and fluid. The traditional analysis methods of porous media, based on the effective stress and Darcy's law, are unable to account for these interactions. For an accurate analysis, the porous media is represented in a fluid-filled porous solid on the basis of the Biot theory of wave propagation in poroelastic media. In Biot formulation, the equations of motion of the soil mixture are coupled with the global mass balance equations to describe the realistic behavior of porous media. Because of irregular geometry, the domain is generally treated as an assemblage of fmite elements. In this investigation, the numerical formulation for the field equations governing the dynamic response of fluid-saturated porous media is analyzed and employed for the study of transient wave motion. A finite element model is developed and implemented into a computer code called DYNAPM for dynamic analysis of porous media. The weighted residual method with 8-node elements is used for developing of a finite element model and the analysis is carried out in the time domain considering the dynamic excitation and gravity loading. Newmark time integration scheme is developed to solve the time-discretized equations which are an unconditionally stable implicit method Finally, some numerical examples are presented to show the accuracy and capability of developed model for a wide variety of behaviors of porous media.
Abstract: In the real application of active control systems to
mitigate the response of structures subjected to sever external
excitations such as earthquake and wind induced vibrations, since the
capacity of actuators is limited then the actuators saturate. Hence, in
designing controllers for linear and nonlinear structures under sever
earthquakes, the actuator saturation should be considered as a
constraint. In this paper optimal design of active controllers for
nonlinear structures by considering the actuator saturation has been
studied. To this end a method has been proposed based on defining
an optimization problem which considers the minimizing of the
maximum displacement of the structure as objective when a limited
capacity for actuator has been used as a constraint in optimization
problem. To evaluate the effectiveness of the proposed method, a
single degree of freedom (SDF) structure with a bilinear hysteretic
behavior has been simulated under a white noise ground acceleration
of different amplitudes. Active tendon control mechanism, comprised
of pre-stressed tendons and an actuator, and extended nonlinear
Newmark method based instantaneous optimal control algorithm
have been used as active control mechanism and algorithm. To
enhance the efficiency of the controllers, the weights corresponding
to displacement, velocity, acceleration and control force in the
performance index have been found by using the Distributed Genetic
Algorithm (DGA). According to the results it has been concluded
that the proposed method has been effective in considering the
actuator saturation in designing optimal controllers for nonlinear
frames. Also it has been shown that the actuator capacity and the
average value of required control force are two important factors in
designing nonlinear controllers for considering the actuator
saturation.
Abstract: This paper presents nonlinear elastic dynamic analysis
of 3-D semi-rigid steel frames including geometric and connection
nonlinearities. The geometric nonlinearity is considered by using
stability functions and updating geometric stiffness matrix. The
nonlinear behavior of the steel beam-to-column connection is
considered by using a zero-length independent connection element
comprising of six translational and rotational springs. The nonlinear
dynamic equilibrium equations are solved by the Newmark numerical
integration method. The nonlinear time-history analysis results are
compared with those of previous studies and commercial SAP2000
software to verify the accuracy and efficiency of the proposed
procedure.
Abstract: Since the actuator capacity is limited, in the real
application of active control systems under sever earthquakes it is
conceivable that the actuators saturate, hence the actuator saturation
should be considered as a constraint in design of optimal controllers.
In this paper optimal design of active controllers for nonlinear
structures by considering actuator saturation, has been studied. The
proposed method for designing optimal controllers is based on
defining an optimization problem which the objective has been to
minimize the maximum displacement of structure when a limited
capacity for actuator has been used. To this end a single degree of
freedom (SDF) structure with a bilinear hysteretic behavior has been
simulated under a white noise ground acceleration of different
amplitudes. Active tendon control mechanism, comprised of prestressed
tendons and an actuator, and extended nonlinear Newmark
method based instantaneous optimal control algorithm have been
used. To achieve the best results, the weights corresponding to
displacement, velocity, acceleration and control force in the
performance index have been optimized by the Distributed Genetic
Algorithm (DGA). Results show the effectiveness of the proposed
method in considering actuator saturation. Also based on the
numerical simulations it can be concluded that the actuator capacity
and the average value of required control force are two important
factors in designing nonlinear controllers which consider the actuator
saturation.
Abstract: The choice of finite element to use in order to predict
nonlinear static or dynamic response of complex structures becomes
an important factor. Then, the main goal of this research work is to
focus a study on the effect of the in-plane rotational degrees of
freedom in linear and geometrically non linear static and dynamic
analysis of thin shell structures by flat shell finite elements. In this
purpose: First, simple triangular and quadrilateral flat shell finite
elements are implemented in an incremental formulation based on the
updated lagrangian corotational description for geometrically
nonlinear analysis. The triangular element is a combination of DKT
and CST elements, while the quadrilateral is a combination of DKQ
and the bilinear quadrilateral membrane element. In both elements,
the sixth degree of freedom is handled via introducing fictitious
stiffness. Secondly, in the same code, the sixth degrees of freedom in
these elements is handled differently where the in-plane rotational
d.o.f is considered as an effective d.o.f in the in-plane filed
interpolation. Our goal is to compare resulting shell elements. Third,
the analysis is enlarged to dynamic linear analysis by direct
integration using Newmark-s implicit method. Finally, the linear
dynamic analysis is extended to geometrically nonlinear dynamic
analysis where Newmark-s method is used to integrate equations of
motion and the Newton-Raphson method is employed for iterating
within each time step increment until equilibrium is achieved. The
obtained results demonstrate the effectiveness and robustness of the
interpolation of the in-plane rotational d.o.f. and present deficiencies
of using fictitious stiffness in dynamic linear and nonlinear analysis.
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.