N.J. Tarp-Johansen

Partial Safety Factors and Characteristic Values for Combined Extreme Wind and Wave Load Effects

Background: The present paper regards the concerted action of wind and wave loads on offshore wind turbines in the extreme storm event. The load combination problem involves the definition of the characteristic loads and safety factors. In wind engineering and offshore engineering well established practices for the definition of characteristic values and safety factors for wind and wave loads separately exist. The aim is to investigate the possibility of making a simple merger of these existing practices into a possibly conservative design rule. Method of Approach: The paper applies a simplified probabilistic approach giving an understanding of how the merging can possibly be established and finally gives first guidance on the choice of characteristic values and safety factors. Results and conclusions: Under the assumptions made herein, it is made probable that a simple combination rule can be established.

White noise excited non-ideal elasto-plastic oscillator

SummaryTwo sets of 50 samples of the displacement response of the top traverse relative to the second traverse of an experimental shear frame with three traverses subject to white noise base shaking of two different intensities have been recorded at Institut für Allgemeine Mechanik in 1995, and are in file available for analysis. The column connection between the two top traverses were made of aluminum with a linear-elastic non-ideal plastic behavior, and the columns were therefore renewed after each experiment. The two other connections were made of steel with a purely linear-elastic behavior. By use of the measured displacement-retaining force relation for the aluminum connection the plastic displacement responses were isolated from the sample records. From the obtained samples of plastic displacement records various distributions were estimated as well as the time development of the variance of the plastic displacement process.This paper presents a determination of the experimentally estimated statistical properties of the plastic response by use of Slepian model process theory as the basis for a numerical simulation algorithm. Solely the given defining parameters of the experimental frame are used in the calculations, i.e. the given displacement-retaining force relations, the traverse masses, the modal damping ratios for the vibrations within the elastic domain, and the two white noise excitation intensities, all as measured.First the Slepian model process method is applied to a single degree of freedom oscillator with linear-elastic non-ideal plastic displacement restoring force relation. The method is based on a direct generalization of the Slepian model process method that quite successfully has been developed for the linear-elastic ideal-plastic oscillator. Next the method is modified to be applicable on an oscillator of more than one degree of freedom. Applied to the experimental frame the calculations give excellent predictions of the main distributional properties of the plastic displacement process.

Time between plastic displacements of elasto-plastic oscillators subject to Gaussian white noise

A one degree of freedom elasto-plastic oscillator subject to stationary Gaussian white noise has a plastic displacement response process of intermittent character. During shorter or longer time intervals the oscillator vibrates within the elastic domain without undergoing any plastic displacements. These pieces of elastic response cannot be distinguished from conditional Gaussian response samples given that they are within the elasticity limits. Therefore, suitable Gaussian process theory can be applied to these pieces. Typically the plastic displacements occur in clumps of random plastic displacements alternating in the two opposite displacement directions. These plastic displacements can be evaluated with respect to distribution by use of Slepian model process considerations and simulation. This paper deals with the problem of determining an accurate evaluation of the distribution of the waiting time between the clumps of plastic displacements. This is needed for a complete description of the plastic displacement process. A quite accurate fast simulation procedure is presented based on an amplitude model to determine the short waiting times in the transient regime of the elastic vibrations existing from a clump of plastic displacements has terminated and until approximate stationarity has been reached. Beyond this regime an additional waiting time is generated from an exponential distribution consistent with the upper tail of the waiting time distribution.

Bayesian soil assessments combining prior with posterior censored samples

Abstract The geotechnical engineer is often faced with the problem of how to assess the statistical properties of a soil parameter on the basis of a sample measured in-situ or in the laboratory with the defect that some values have been replaced by interval bounds because the corresponding soil parameter values have turned out to exceed the capacity of the measuring instrument. Given such a censored sample the problem is to estimate the mean value, variance and certain fractiles of the distribution of the soil parameter as it would be measured by an instrument of unrestricted range. In many situations only a small censored sample is given. To estimate the characteristic value defined as a lower fractile value corresponding to a codified probability value, the geotechnical engineer is thus urged to supplement the information from the measurements at the actual location by considering whatever prior knowledge is available about the soil parameter distribution. The present paper shows how a characteristic value by computer calculations can be assessed systematically from the actual sample of censored data supplemented with prior information from a soil parameter data base.

Mechanical Characteristics of Some Deepwater Floater Designs for Offshore Wind Turbines

This paper presents an initial study of the mechanical characteristics of some deepwater floater designs for offshore wind turbines. Three different concepts (NREL TLP Dutch Tri-floater, and Japanese SPAR) are summarized, based on data from the available studies. A 5 MW Horizontal Axis Wind Turbine is used for the reference wind turbine and the steady wind load is calculated from the Blade Element Momentum method. These three concepts are simplified to 2D models and the static analyses of NREL TLP and Dutch Tri-floater are compared. The 2D NREL TLP model is selected for dynamic analysis, in which: (1) regular and irregular wave loads are calculated from the Morison equation for the relative motions in the time domain; (2) Airys linear wave theory is applied to compute the wave kinematics; (3) The 10-minutes irregular waves are realized from the JONSWAP spectrum. For comparison, the same 2D NREL TLP floater model is also developed and implemented as a subsystem in the wind turbine simulation program, HAWC. The HAWC results are compared with those from our model.

An Approach to Optimizing the Structural Reliability and the Reliability of the Control and Safety System of Wind Turbines

From the past experience one may anticipate that the reliability of the control and safety system of wind turbines (WTBs) for electric power generation is too low compared to the structural reliability. May the failure probabilities of these two sources of failure be balanced and may the total probability of failure be possibly reduced (optimized), then it must be expected that the price of the turbines may be reduced. Such a result would especially be relevant to the planned enlargement of the Danish offshore wind turbine farms. In this paper we explore whether such an imbalance is really present.

Slepian Approach to a Gaussian Excited Elasto-Plastic Frame Including Geometric Nonlinearity

Taking geometric non-linearity into account, an oscillator inthe form of a portal frame with a rigid traverse and withideal-elastic-ideal-plastic clamped-in columns behaves under horizontalexcitation as an ideal-elastic-hardening/softening-plastic oscillatorgiven that the columns carry a tension/compression axial force. Assumingthat the horizontal excitation of the traverse is Gaussian white noise,statistics related to the plastic displacement response are determinedby use of simulation based on the Slepian model process method combinedwith envelope excursion properties. Besides giving a physical insight,the method gives good approximations to results obtained by slow directsimulation of the total response. Moreover, the influence of a randomlyvarying axial column force is investigated by direct responsesimulation. This case corresponds to parametric excitation as generatedby the vertical acceleration component in an earthquake.