Keywords: shear lag, latin hypercube sampling, finite element analysis.

The parametric study is carried out in order to deal with shear lag effect of plate structures, especially box girders. Commercial finite element software ANSYS in combination with Latin Hypercube Sampling Method is used in parametric study to analyse the influence of different geometry on shear lag effect. In this case, Latin Hypercube Sampling Method is used for planning the strategy of parametric study, not for generating random variables. The sensitivity and the influence of all parameters is analysed within one procedure and the key geometrical parameters with the largest influence are immediately identified. Compared with other parametric studies, the present strategy can deal with the influence of all parameters directly and can give us more sophisticated information about the shear lag effect. The efficiency is demonstrated on a typical box girder.

Shear lag phenomena were recognised and studied many years ago. First studies were based on the beam or plate theories. Later investigation was performed using advanced techniques and 3D finite elements. Improved strategies like adaptive finite element analysis enabled us to obtain results with predetermined accuracy together with a reasonable amount of computational effort. Various parametric studies [1] investigated the effect of different geometry, loading and boundary conditions.

As modelling efforts expand to a broader spectrum of problems, a judicious selection of procedures is required. Among others, the parametric studies should be optimised. Generally, all input parameters that may be important for the process being modelled should be taken into account in parametric studies. Frequently, the numbering of parameters is in hundreds. All possible values of all parameters must be combined with each other and the simulation run with the set of input values must be performed. The combination of many parameters and the complex relationship among the variables result in a time consuming process because thousands of simulation runs must be performed. Because of the expense and time involved on the computer, only a limited number of runs is feasible. The present methodology was formerly proposed by Florian. For input parameters with values (called now stratum) the total number of possible combinations equals . To limit the number of runs, only some of possible combinations (totally ) will be taken into account and the number of runs will dramatically drop to . In order to choose the appropriate combinations, every stratum of each parameter must have some possibility of appearing in simulation coupled with each stratum of each other parameter. Therefore, a random combination of the different strata of the input parameters is required. If there are only two input parameters this method of sampling is known in sample surveys as a "Latin Square". Because we are using more than two parameters, a different, more general method should be used. Among others, sampling procedure Latin Hypercube Sampling, see McKay et al. [2], and Updated Latin Hypercube Sampling, see Florian [3] are the most appropriate ones.

The methods use the same theoretical background. They belong to the family of sampling techniques utilised in reliability analyses. That is, they are used to solve problems in which the input variables are random variables. In the case of parametric studies, there are no random inputs. Thus the methods are not used to generate random variables but for planning the optimal strategy of parametric study resulting in a limited number of necessary simulation runs.

The present parametric study proved that the sensitivity and the influence of the geometrical parameters can be analysed within one procedure using Latin Hypercube Sampling Method. The most important parameters with the largest influence can be immediately identified. The present methodology can deal with the influence of all selected parameters directly and can give us complex information about the shear lag effect.

Numerical analysis confirmed the expected results for a simple box girder. Further research will study more complex structures under different loads and boundary conditions and may detect an unexpected influence of any input parameter.

1

C.K. Lee, G.J. Wu, "Shear lag analysis by the adaptive finite element method. 1: Analysis of simple plated structures", Thin-Walled Structures 38, 285-309, 2000. doi:10.1016/S0263-8231(00)00043-4

2

M. McKay, R.J. Beckman and W.J. Conover, "A Comparison of Three Methods for Selecting Values of Input Variables in the Analysis of Output from a Computer Code", Technometrics, 2, 239-245, 1979. doi:10.2307/1268522

3

Florian, A., "An Efficient Sampling Scheme: Updated Latin Hypercube Sampling", J. Probabilistic Engineering Mechanics, 7(2), 123�130, 1992. doi:10.1016/0266-8920(92)90015-A

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