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2017 Vol. 38, No. 4
Published: 2017-08-28
287
Wavelet Methods and Applications in Nonlinear Mechanics Problems
Wavelet analysis is a mathematical branch developed in the past several decades, which is known as the so-called "numerical microscope". Wavelets have the unique mathematical property of multiresolution analysis. When using wavelet and scaling functions as basis, they have excellent mathematical characteristics of orthogonality, compactness, symmetry, low-pass filter, approximate linear phase and interpolation etc. These properties brought new opportunities to developing advanced numerical techniques on accurately and efficiently solving differential equations in nonlinear mechanics problems. Since the 1990s, numerical methods such as wavelet Galerkin method, wavelet collocation method, wavelet finite element method and wavelet boundary element method etc. have been constructed and successfully applied to the quantitative research of mechanical problems. Most importantly, wavelet analysis provides a totally new way to develop robust and adaptive methods for efficiently solving mechanical problems with large local gradients, and to propose closure algorithms to uniformly solving problems with strong nonlinearity. Problems with these two types of features are usually very difficult to deal with by using most traditional methods. Starting from the review of historical background and theory of multiresolution analysis, this review systematically discusses how specific mathematic property of the wavelets can merit high efficiency and accuracy of the wavelet-based method, and why the Coiflet-based method is a good choice in developing advanced numerical algorithms for solving nonlinear differential equations. Also, this paper analyzes the existing numerical methods related to wavelets and summarizes the advantages, disadvantages and possible development directions of wavelet based methods. Especially, this paper discusses the closed-form numerical algorithm based on the Coiflets for solving nonlinear mechanical problems in detail. An example on the shallow water equation demonstrates that such a method has the ability to capture major pattern characteristics of the solution even under very coarse space-time meshes. Our ultimate goal is to eventually provide a valuable reference to the further development of wavelet methods and their applications in various complex mechanics problems.
2017 Vol. 38 (4): 287-311 [
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312
On-Line Monitoring Technologies for Complex Structural Damage Identification Based on Low-Frequency Structural Dynamic Signals and Ultrasonic Guided Waves
n the recent past thirty years, great progress has been made for various effective on-line monitoring technologies of engineering structural damage based on various measurement data. Due to countless research outcomes in this field, the present review article will be only limited to the introduction and summary on those on-line damage monitoring methods or technologies using structural dynamic data. It mainly contains the following two aspects. First, we introduce various technologies using low-frequency structural low-frequency dynamic signals to carry out the on-line monitoring of large-scale complex structures in various engineering fields, e.g., civil, aerospace, etc. Especially, we will focus on the fundamental theories, methods and applications of those technologies based on the low-frequency structural vibration data. Second, we will introduce various on-line technologies for structural damage identification and monitoring based on high-frequency structural high-frequency dynamic signals. We mainly introduce and describe those technologies based on ultrasonic guided waves and their applications in detail, which have been developed quickly in the recent past more than ten years. This article introduces and analyzes the application scopes of the various above above-mentioned various technologies. Moreover, for different application situations, their advantages and drawbacks are described. Finally, we give an outlook to the trend of development about some future methods and technologies in this field.
2017 Vol. 38 (4): 312-347 [
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348
On the power-law relation between retardation time and creep load for rigid inclusions filled a polymer composite
A new type polymer composite was developed by filling short stainless steel fibers (SSFs) into polypropylene (PP). The creep behavior of the composite material was studied under different level of creep load. The experiment shows that a nonlinear relationship exists between the creep strain and creep load under the same loading time, and such a phenomena could not be explained by the linear viscoelastic theory. In order to analyze the phenomena, the view of creep load dependence of retardation time was taken into account. It was found that a linear relation between the retardation time and creep load in the logarithmic coordinate system, and thus the power-law relation was proposed to describe the relation between the retardation time and creep load. Further analysis indicated that the increase of retardation time with creep load is induced by micro-damage evolution.
2017 Vol. 38 (4): 348-358 [
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359
Interfacial crack propagation study for sandwich composites with visco-elastic core after unloading
Sandwich plate with steel faceplates and polyurethane elastomer core (SPS) is a new type of composite which is wildly used in shipbuilding and civil engineering. Lightweight, high strength, excellent fatigue resistance and good workability make SPS have more application prospects. Debonding is one of main failure modes of SPS under bending loads and interface strength is the key factor to determine bending strength. In this paper, 3-points bending tests are carried out to investigate bending performance of SPS. Different failure modes are obtained and discussed with different manufacture ways. It can be observed from bending tests that when the deflection exceed a certain range, the crack will appear in loading process. And it will lead to debonding of whole interface between faceplates and polyurethane (PU) core in the following unloading process. The reason of this phenomenon is PU core has viscoelasticity characteristic and lower interface strength, so the debonding process does not happen immediately after tests, but take a period of time before upper faceplate debonds from the core. In case of cohesive interface manufactured by glue, the core will be tear out at location of 1/3 length of specimen. These phenomenon are illustrated by a series of analysis: Firstly, deflection difference between upper faceplate and under faceplate is calculated by introducing the theory of beam on elastic foundation. Secondly, plastic analysis of sandwich plate is carried out and cohesive strength analysis is utilized to evaluate the critical state of crack propagation. Finally, critical interface crack lengths are obtained for different core types and at same time, relationship between different bending angle and crack length is also given to address interactions between critical crack length and cohesive stress. The results show that the former analysis based on interface cohesive strength can illustrate the characteristics of interface delay debonding for sandwich plate with viscoelastic core.
2017 Vol. 38 (4): 359-368 [
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Plastic failure analysis of a reactor pressure vessel subjected to pressurized thermal shock
Pressurized thermal shock (PTS) will produce a great challenge on the integrity of a reactor pressure vessel (RPV), especially in the beltline region around the inlet nozzles. So it is necessary to study the influence of PTS on the ultimate bearing capacity of a reactor pressure vessel (RPV) with defects. The current analysis methods are based on the assumption of linear elasticity or small range yield, and there is little research on the crack growth behavior and the ultimate bearing capacity of the RPV structure. Considering that the transient temperatures are above the nil-ductility reference temperature, the nonlinear material properties are adopted to simulate the combined temperature field and stress field of a real RPV. By using the XFEM, the process of the crack propagation in the nozzle region is simulated, and the critical crack sizes under the PTS are obtained. The results show that the thermal stress effect is significant in the early stage of the PTS transient, and the peak stress caused by thermal-mechanical coupling is very likely to cause structural failure. The numerical results obtained by the direct coupling method are in good agreement with the results obtained by the indirect coupling method, and the calculation efficiency of the latter is higher. In the plastic limit bearing condition, the crack tip close to the inner wall is easy to expand. For the crack tip which is far from the inner wall, the possibility of crack propagation is relatively low due to the weak thermal shock effect. With the decrease of the base wall thickness, the allowable crack sizes are drastically reduced, and the extent of the steady crack propagation is obviously reduced until the ultimate bearing state is reached. This study provides an important reference for the integrity and reliability assessment of the cracked RPV in the thermo-mechanical coupling field.
2017 Vol. 38 (4): 369-378 [
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