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However, due to its discontinuity of materials, frictional contact, mechanical micro-slippage along the interface, the interface becomes the main sources of structural nonlinearity and uncertainties.
The value of pretension force [7] can be measured directly by the elongation of threaded rod and ultimate preload in bolted joint can be given by value of yield strength of bolt material and described as Eq.(1) (1) Where KP is the constant coefficient from 0.75 to 0.99; As is the tensile stress area; SP is the proof strength of the bolt material.
Franco, Determination of Valanis model parameters in a bolted lap joint: Experimental and numerical analyses of frictional dissipation, International Journal of Mechanical Sciences. 89 (2014) 289–298
Nash, Analysis of externally loaded bolted joints: Analytical, computational and experimental study, International Journal of Pressure Vessels and Piping. 86 (2009) 420–427
[6] Lu Aihong, Xu Jinhai, Liu Haishun, Effect of a preload force on anchor system frequency, International Journal of Mining Science and Technology. 23 (2013) 135–138

It is supposed that the shell, tube sheet and tubes of the heat recovery boiler are made of the same material Q345R, the material properties [8] are shown in Table 2.
Acknowledgments The work is supported by the National Natural Science Foundation of China (No. 51376163 & No. 51476147).
Z., Pan, Pressure Vessel Materials Handbook - Carbon Steel and Alloy Steel, Chemical Industry Press, Beijing, China, 2000
Sih (Eds.), Structural Integrity in Nuclear Engineering, East China University of Science and Technology Press, Shanghai, 2011, pp. 319-323
A., Heat Exchanger Tube Sheet Temperatures, Journal of Applied Mechanics, (1948) 377-385

Chinese Journal of Mechanical Engineer Vol.37 (2001), p.109
Journal of Sound and Vibration Vol.58 (2003), p.321 [6] C.K.Toh: J.
Material and Design Vol.27(2004), p.107
Material and Design Vol.30(2004), p.41
[8] Y.WANG and H.H.HUANG: Journal of Central South University Vol.40(2009), p.1604

The transducer array is respectively assembled with the PMNT /epoxy composites and PZT5/epoxy piezoelectric composite materials.
Now new piezoelectric materials have been widely researched,and piezoelectric devices have widely been used in many fields.
In the late 70s of last century, in order to overcome the piezoelectric acoustic transducer applications insufficient, the University of Pennsylvania and other research institutions began to develop piezoelectric composite materials which are made ​​of a piezoelectric material and a polymer, which has a certain way of communicating, a certain ratio of the volume or weight, and certain spatial geometric distribution.
In the 90s of last century, Relaxor ferroelectric single crystals was developed, which is a new generation of piezoelectric functional materials because of their excellent piezoelectric properties.
Acknowledgements This work was supported by the National Science Foundation of China (Grant No.10974036 ) References [1] Guidong Luan, Jinduo Zhang, Renqian Wang , piezoelectric transducer and transducer array, Peking University Press, 1987 In Chinese [2] R.E.Newnham, et al., Composite Piezoelectric Transducers, Materials in Engineering, 1980, 2, 93-106 [3] R.E.Newnham,D.P.Skinner,L.E.Cross, Connectivity and Piezoelectric- Pyroelectric Composites,Mat.Res.Bull.,1978,13, 525-536 [4] LI xiao-bing, et al., Growth, Properties and Applications of relaxor-based Ferroelectric Single Crystals, journal of synthetic crystals,Vol.41,Supplement,August,2012 [5] Kei C.

In undamaged case, the isotropic complementary energy of materials can be described as
Mechanical Parameters of Materials.In this model, the trabecula is AC20, its elastic modulus E=1200MPa and the Poisson’s ratio υ=0.3.
Acknowledgements This work was financially supported by the Liaoning Province Natural Science Foundation (201102178).
Journal of Highway and Transportation Research and Development, 2012, v.29(1): 34-37
Journal of Shenyang Jianzhu University (Natural Science).2013,29(1):56-64

While B=B1, h=h1: （11） It can be found from Eq.(13), the is only determined by the r value coming from the different direction, then, using to evaluate the materials anisotropy is rational and effective.
It also can be obtained from Fig.4 and Fig.5, for 08Al material and for L3 material when displacement is 3mm (i.e. strain equals to 0.2), respectively.
International Journal of Mechanical Sciences[J], 2011,53: 338–347 [3] Srbislav Aleksandrović, Milentije Stefanović, Dragan Adamović, Vukić Lazić.
Journal of Mechanical Engineering[J], 2009,55(6) 392-399 [4] Mihaela TEACĂ, Marion MARTINY, Gérard FERRON, Marioara ABRUDEANU.
Journal of Harbin Institute of Technology (New Series)[J], 2007,14(6)752-755 [6] Hill R.

Journal of Materials Engineering and Performace, Vol 16 (No. 6), 2005, p 681-685
Koss, Ed., The Materials Society, 1993, p 335-346
Journal of Materials Engineering and Performance, Vol 14 (No. 6),2005, p. 799-811
Journal of Materials Engineering and Performance, Vol 16 (No. 6), 2005, p 788-791
Materials Science and Engineering A , Vol 490, 2008, p369–377

Materials and Methods It is proposed to use three coefficients to determine the geometric dimensions of filter boxes: – the comfort coefficient, which allows for the assessment of the impact of the box's geometric dimensions on breathing resistance.
Materials Science Forum. 1038 (2021) 221–232. https://doi.org/10.4028/www.scientific.net/MSF.1038.221 [2] Małgorzata, О., Serhii, С., Radchuk, D., Deryugin, O., Sharovatova, O., Evaluation of properties of elastomeric head straps of filtering facepiece respirators.
Journal of Applied Mathematics and Physics. 7 (2019) 1920–1928.
In IOP Conference Series: Earth and Environmental Science. 1348 1 (2024) 012014.
Materials Science Forum. 1141 (2024) 35–42.

In this paper board hammer, shaft, coal and gangue were defined as research objects, properties of the materials were listed in Table 1.
Using regular Eight-node hexahedral element to mesh the board hammer, shaft and impact materials, the specific shapes were shown in Fig. 1.
coal gangue Fig. 2 Contact Forcing Process for Material It can be seen from Figure 2: As the materials properties were different, both the impact time and the peak of impact forces were has big difference even the impact velocity and materials size were the same.
Acknowledgements The authors would like to express their grateful for the financial support of the National Natural Science Foundation of China (51005232) and the Natural Science Fund of Jiangsu Province (BK2009098).
[5] Jun Liu: Chinese Journal of Rock Mechanics and Engineering, 2(2004), pp. 635-640.

(2) Resource properties: The division hierarchical of resource properties is mainly based on the appearance of manufacturing resources, materials, uses and sources
Dividing by the level of the raw material, the specific raw material instance can be obtained.
Yuchen, Research on manufacturing resource modeling based on the O–O method, Journal of Materials Processing Technology, vol. 139, pp. 40-43, 2003
KorkusuzPolat, Enterprise knowledge management model (EKMM) in strategic enterprise resource management (SERM), Procedia - Social and Behavioral Sciences, vol. 24, pp. 870-879, 2011
Wysk, Resource modeling for the integration of the manufacturing enterprise, Journal of Manufacturing Systems, vol. 19, pp. 407-427, 2001