Supporting Document for Surrogate Model Construction of Welded HSS Tubular Y-Joints: Preliminary version
Garifullin, Marsel; Jokinen, Timo; Heinisuo, Markku (2016)
Tampere University of Technology. Department of Civil Engineering
2016
Talouden ja rakentamisen tiedekunta - Faculty of Business and Built Environment
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Julkaisun pysyvä osoite on
https://urn.fi/URN:ISBN:978-952-15-3700-4
https://urn.fi/URN:ISBN:978-952-15-3700-4
Tiivistelmä
Tubular structures with welded joints are used in the wide range of structural applications. The most typical application is tubular trusses. The structural analysis model is frequently constructed using beam finite elements, and the braces are connected to the chords using hinges. In reality, the welded joint does not behave as a hinge when it is loaded by the moment. The joint has resistance against the moment, but in the joint area deformations may occur both at the brace and at the chord, so the stiffness against the moment has to be taken into account in the global analysis of the structure. In the EN 1993-1-8 (2005) only the moment resistance is given for the joint where the angle between the brace and the chord is 90 degrees. In (Grotmann and Sedlacek, 1998) there is the equation which can be used to calculate the initial rotational stiffness for the same case, angle 90 degrees.
When aiming to economic and environmental friendly design the stiffness of the joints must be taken into account. This is especially true when using high strength steel in structures, because then buckling at the ultimate limit state and deflections and vibrations in the serviceability limit state are often critical. In (Boel, 2010) and (Snijder et al., 2011) it has been shown that the rotational stiffness of the welded tubular joint is the main parameter when considering buckling of members of tubular trusses. However, this information is very limited, as given above.
In design it is possible to define the rotational stiffness for the joint using comprehensive finite element analysis (FEA). In practice, this is impossible, especially when performing optimization of structures when the structural analysis must be done thousands and thousands times. In order to avoid these computationally heavy calculations so called surrogate models (or meta models) have been developed. Surrogate models have been used widely in the aerospace applications (Roux et al., 1998), (Jin et al., 2001), (Queipo et al., 2005), (Kleijnen, 2008), (Müller, 2012). Civil engineering applications can be found, too (Mukhopadhyay et al., 2015). In (Díaz et al., 2012) there are 9 references presented (Yun et al., 2008), (Jadid and Fairbairn, 1996), (Anderson et al., 1997), (Stavroulakis et al., 1997), (De Lima et al., 2005), (Guzelbey et al., 2006), (Pirmoz and Gholizadeh, 2007), (Salajegheh et al., 2008), (Kim et al., 2010) dealing with steel structures using surrogate models. In (Díaz et al., 2012) the optimum design of steel frames is presented using semi-rigid joints and surrogate models.
The standard steps in the construction of the surrogate model are:
· Design of experiments (DOE);
· Surrogate model construction;
· Surrogate model validation.
Moreover, the fourth step is the fidelity validation, but it is not needed here
When aiming to economic and environmental friendly design the stiffness of the joints must be taken into account. This is especially true when using high strength steel in structures, because then buckling at the ultimate limit state and deflections and vibrations in the serviceability limit state are often critical. In (Boel, 2010) and (Snijder et al., 2011) it has been shown that the rotational stiffness of the welded tubular joint is the main parameter when considering buckling of members of tubular trusses. However, this information is very limited, as given above.
In design it is possible to define the rotational stiffness for the joint using comprehensive finite element analysis (FEA). In practice, this is impossible, especially when performing optimization of structures when the structural analysis must be done thousands and thousands times. In order to avoid these computationally heavy calculations so called surrogate models (or meta models) have been developed. Surrogate models have been used widely in the aerospace applications (Roux et al., 1998), (Jin et al., 2001), (Queipo et al., 2005), (Kleijnen, 2008), (Müller, 2012). Civil engineering applications can be found, too (Mukhopadhyay et al., 2015). In (Díaz et al., 2012) there are 9 references presented (Yun et al., 2008), (Jadid and Fairbairn, 1996), (Anderson et al., 1997), (Stavroulakis et al., 1997), (De Lima et al., 2005), (Guzelbey et al., 2006), (Pirmoz and Gholizadeh, 2007), (Salajegheh et al., 2008), (Kim et al., 2010) dealing with steel structures using surrogate models. In (Díaz et al., 2012) the optimum design of steel frames is presented using semi-rigid joints and surrogate models.
The standard steps in the construction of the surrogate model are:
· Design of experiments (DOE);
· Surrogate model construction;
· Surrogate model validation.
Moreover, the fourth step is the fidelity validation, but it is not needed here