Proposed formulas for evaluation of the equivalent material properties of a multiholed structure
Introduction
In this study, a multiholed plate is regarded as a single plate with numerous circular holes that are regularly arranged across it. Multiholed structures are used extensively in various engineering fields. In offshore structures, multiholed structures are used as heat shields against fire action and as perforated blast walls that function as a passive mitigation system by disrupting explosive pressure. In the nuclear field, multiholed structures express their structural characteristics in nuclear reactors and are mainly used to provide structural support and to facilitate the flow-passage of coolants. In civil engineering, multiholed structures are used as building components for various engineering purposes.
The application of multiholed structures is limited because their failure can directly affect system operation failure. Therefore, many engineers and designers continue to perform structural analysis and assessment of multiholed structures and focus upon numerical analysis of the nonlinear response and stress concentration of multiholed plates for safety design and operation. In the design of multiholed structures, it is necessary to define equivalent material properties to structural behaviour. However, limited information is available in the literature to determine the equivalent material properties of multiholed structures.
A theoretical method was developed to determine the equivalent elastic properties of a perforated plate, and several validation experiments were carried out (Bailey and Hicks, 1960). They successfully obtained design curves to determine the equivalent elastic properties of the perforated plate. However, the nonlinear equivalent material properties of the perforated plate were not considered. Choi et al. (1998) presented a finite-element (FE) modal analysis of a perforated plate with diagonal and square penetration patterns, and an attempt was made to put the equivalent elastic constants into the solid plate using modal analysis to compare the behaviour of the perforated plate with its original properties. However, the method for determination of the equivalent material properties was not mentioned. Although Appendix A to Section III of the ASME (2004) contained a method for calculating the equivalent elastic constants of multiholed plates, the methods for determining the equivalent yield strength, equivalent ultimate strength and equivalent fracture strain for each specified multiholed plate were not presented. The imperfection of the ASME rule for modal analysis was realised, and several new formulas were developed to determine the equivalent Young's modulus of a thin multiholed plate by means of modal analysis (Jhung and Jo, 2006). A series of FE analyses for a triangular perforated circular plate were numerically performed using an axisymmetric model. Based on the simulation results, several equations were proposed to determine the equivalent elastic material properties and nonlinear equivalent material properties of the perforated plate. Kasahara et al. (2007) also clarified that the equations were only geometric functions and that they were independent of both the constitutive equation and the material type without experimental investigation. The buckling strength of steel plates with a circular hole were analysed numerically under axial compressive loading along their short edges by varying the hole size and performing compression with elastic buckling strength with plasticity correction (Paik, 2007). However, in this paper, only one hole on the plate was considered. Meanwhile, the buckling and ultimate strength of perforated plate panels with an opening were investigated experimentally and numerically subject to axial compression, and new design-formula solutions with important parameters of influence were derived (Kim et al., 2009). However, only one opening on a plate was considered for analysis of the compressive strength of perforation. The stability of a biaxial loaded square plate with a single central hole was numerically studied (El-Sawy and Martini, 2010), and the families of the design curve were generated to define the buckling stress for the various hole sizes, but the necessary experimental validation was not presented.
In this study, the linear and nonlinear equivalent material properties of a multiholed plate of stainless steel 316L with either a diagonal or square pattern were mainly examined by means of quasi-static analysis using both experimental and numerical methods. A series of nonlinear FE computations were performed with varying thicknesses, pitch ratios and ligament efficiencies. The sensitivity of the specified geometry parameters on the equivalent material properties was then analysed and is discussed in detail in this paper. Finally, eight types of formulas derived as a function of the ligament efficiency are proposed.
This paper also presents six groups of experimental investigations conducted with various types of multiholed plates. One set of experiments was used to validate the modelling technique, and the remaining experiments compared the proposed formulas to enhance their reliability. Meanwhile, the proposed formulas were also compared with the current rules and studies on the equivalent material properties of a multiholed plate to further improve their applicability. This series of validations with various methods demonstrated that the proposed formulas provide some useful support for the nonlinear analysis of large perforated structures. These proposed formulas will be very useful for structural designers for easy determination of the additional thickness of perforated structure that is required to provide the same properties as an unperforated plate at the same scale.
Section snippets
Experimental modal investigations
A series of experimental investigations of the tensile properties of the multiholed specimen were carried out at the Korea Ship and Offshore Research Institute at Pusan National University to determine the equivalent material properties of the multiholed structure.
Target specimen
A multiholed specimen of SUS316L-60°-20%-0.12-0.53-01 was used as the target specimen to verify the numerical model. The detailed configuration of the target specimen is shown in Fig. 6. The thickness of the specimen is set at 1.0 mm.
Material modelling
Stainless steel 316L is an austenitic stainless steel that is widely used in offshore installations and ship structures. This type of stainless steel is also extensively used in many engineering applications for its resistance to corrosion, improved welding
Proposed multihole formulas based on numerical results
In this section, the geometric parameters of the multiholed plate are considered, and the influence of each geometric parameter on the structural behaviour of the multiholed plate is investigated with the verified FE model. Finally, the proposed formulas are derived as a function of the ligament efficiency by fitting the curve, which can determine the equivalent Young's modulus, the equivalent yield strength, the equivalent ultimate strength and the equivalent fracture strain of the multiholed
Conclusions
Modelling the details of large-scale perforated structures and the construction of fine mesh around the circular holes is quite complex. Moreover, the relative simulation requires significantly more time to run for a perforated structure than for an unperforated structure. Therefore, it is necessary to study the equivalent material properties of a multiholed plate with diagonal or square penetration patterns and to derive formulas to effectively predict the equivalent material properties of a
Acknowledgements
This research was supported by the Components & Materials Technology Development Programme (Grant no.: 10043799) which funded by the Ministry of Trade, Industry & Energy (MOTIE), Korea.
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