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The brightest trait of the degenerated virtual laminated element is virtual lamination, so the calculation of the stiffness matrix can be divided into different blocks and different materials, and the blocks with no material are virtual blocks, the stiffness of which are set to be zero.
Hence, since an element could contain multiple materials or even no material, the work is much easier when we separate the structure into elements, especially for complicated structures such as box girder, the number of elements can be remarkably reduced.
The formula to calculate the stiffness matrix of an element containing various materials is as follows: (2) In the formula, is the number of material types, is the Jocobi determinant of the coordinate transverse matrix for the very block.
Xu, New laminated block element and its application in engineering[J], China Journal of Highway and Transport, 2002(15)2, pp72-75 [4] Yasuhiro Ohtani and Wai-fah Chen, Multiple Hardening Plasticity for Concrete Materials [J], Journal of the engineering mechanics division, ASCE1988, 114(11) [5] H.C.Wu, J.W.
Xia: Three-Dimensional Non-Orthogonal Smeared Crack Model for Concrete[J],  Journal of Hohai University(Natural Sciences),1999(27)5

Effect of Composition Adjusting Materials on the Cementitious Property of Reconstructed Steel Slag[J].
Journal of building materials,2012,15(3):399-405
Journal of Hazardous Materials, 2008, 152:805811
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Recycle of Converter Slag by High Temperature Carbon Thermal Reduction[J].Journal of materials and metallurgy,2003,2(3):167-172

Materials Science and Engineering: A, 2008, 483: 120-122
Materials Science and Engineering: A, 2000, 283(1): 144-152
Materials Science and Engineering: A, 2009, 506(1): 1-7
Journal of materials science, 1993, 28(3): 677-683
Materials Science and Engineering: A, 2013, 577: 64-72.

The Preisach formalism is used as a basis for a vector model of magnetic hysteresis in soft magnetic materials subject to tensile stress.
Nagao, Magnetic properties of dislocations, in Concise encyclopedia of magnetic and superconducting materials, Ed.
Padovese, Simulation of the Barkhausen Noise using random field Ising model with long-range interaction, Computational Materials Science 44, 850–857(2009) [3] Katsuhiko Yamaguchi, Shinya Tanaka, Osamu Nittono, Koji Yamada, Toshiyuki Takagi, Monte Carlo simulation for magnetic dynamic processes of micromagnetic clusters with local disorder, Physica B 372, 251–255 (2006) [4] B.
Buiron, Magnetic behaviour versus tensile deformation mechanisms in a nonoriented Fe/(3 wt.%)Si steel, Materials Science and Engineering A359, 62-74 (2003) [10] A.
Massalas, Identification of 1D and 2D Preisach models for ferromagnets and shape memory alloys, International Journal of Engineering Science, 40 (20), 2235-2247 (2002) [11] Shuqiang Yang, G.

The piezoelectric properties of PZT thick-films are compared to those of ceramics prepared with the same materials.
Conclusion The efficiency of this simple and low-cost process has been demonstrated with the fabrication of MEMS based on different materials (metals, ceramics, glass, glass-ceramics, etc.).
Piezoelectric materials have been chosen for the processing of actuated MEMS, more precisely anchored bridges andFig. 2: Real part of the ElectroMechanical Impedance (EMI) measurements with the Au/PZT/Au microceramic bonded on the metallic structure.
Lucat, Journal of European Ceramic Society, 25, 2105-2113, (2005) [4] S.
Lucat, International Journal of Applied Ceramic Technology,1-10, DOI: 10.1111/ijac.12006 (2013)

Low cost raw materials, e.g., ceramic oxides, can be used.
Nasiri- Tabrizi, Mechanochemical synthesis of Al2O3-TiB2 nanocomposite powder from Al-TiO2-H3BO3 mixture, International Journal of Refractory Metals and Hard Materials, 2011, Vol. 29, pp. 244-249
Ataie, Preparation of alumina/titanium diboride nano-composite powder by milling assisted sol–gel method, Journal of Refractory Metals and Hard Materials, 2012, Vol 31, pp. 121–124
Speyer, Aluminothermic reaction path in the synthesis of a TiB2-Al2O3 composite, Journal of Materials Research, 1997, Vol. 12, pp. 1681-1684
Meyers, Combustion synthesis/densification of an Al2O3-TiB2 composite, Materials Science and Engineering A, 2001, Vol. 311, pp. 83-99

It includes multilayer circuit board, filling and sealing materials and shell form multiple order transfer function, which has inevitable effects on sensor frequency response characteristic.
Table 1 Corresponding parts materials shell Potting material material name LY12 epoxy resin-5288 young modulus /MPa 73000 3500 poisson's ratio 0.35 - density /tonne·mm-3 2.78e-009 1.26e-009 Using material properties and modal model, through the axis algorithm, the system of natural frequency Test results are shown below Table 2.
Acknowledgements This work was financially supported by National Key Laboratory of Electronic Testing Technology Foundation of China under Grant No.9140C1204051010 and School youth science fund.
The blast vibration testing technology several basic problems , Journal of Blasting, vol. 2, pp.5-8, 2002
Used in geophysical exploration of MEMS acceleration sensor ,Journal of Transducer and Microsystem Technologies. vol.12,pp.1-4,2002

Experiment Materials.
Materials and Design, 2013, 52:1018-1026
Materials and Design, 2014, 59: 130-134
Journal of Changchun University of science and technology (Natural science edition), 2012, 35(1):109-111
Journal of Shanxi university (Natural science edition), 2013, 36(3):431-435

Materials and methods Materials Silver carps (1kg average) were bought alive from local fishery.
Journal of Food Science Vol. 67 (2002), p2962-2967 [6] Siddaiah, D., Reddy, G.
Journal of Food Science Vol. 63 (1998), p215-218 [11] Benjakul S., Visessanguan W., Thongkaew C.
Journal of Food Science Vol. 70 (2005), p298-306 [16] Yongsawatdigul, J., Park, J.
Journal of Food Science Vol. 69 (2004), p499-505

Raw materials.
Jiang, et al, Life cycle assessment of typical building thermal insulation materials in China, New Building Materials,40(2013) 41-44
Nie, The basis of environmental material, Science Press, Beijing, 2003
Progress in materials Science and Engineering, 2006
Gong, et al, Environment Impact of Freight Transportation in China, Materials Science Forum, 787(2014) 144-151