力学进展

BEYOND PERTURBATION: THE BASIC CONCEPTS OF THE HOMOTOPY ANALYSIS METHOD AND ITS APPLICATIONS

2008, 38(1): 1-34. doi: 10.6052/1000-0992-2008-1-J2007-092

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A new and rather general analytic method for strongly nonlinear problems, namely the homotopyanalysis method (HAM), is reviewed. Different from perturbationtechniques, the homotopy analysis method is totally independent ofsmall physical parameters, and thus is suitable for mostnonlinear problems. Besides, different from all other analytictechniques, it provides us a simple way to ensure the convergenceof solution series, so that one can always get accurate enoughanalytic approximations. Furthermore, different from all other analyticmethods, it provides us a great freedom to choose base functions ofsolution series, so that a nonlinear problem may be approximated more effectively. The homotopyanalysis method provides us a completely new way and a differentapproach to solve nonlinear problems, especially those withoutsmall physical parameters. In this review paper, the basic conceptsof the homotopy analysis method and its applications in nonlinearmechanics, physics, chemistry, biology, finance, engineering,computational mathematics and so on are discussed, together withits difference and relationship to perturbation techniques,Lyapunov artificial small parameter method, $\delta$-expansionmethod, Adomian decomposition method, and the so-called homotopyperturbation method.

STRUCTURAL MECHANICS OF LATTICE GRIDS

2008, 38(1): 35-52. doi: 10.6052/1000-0992-2008-1-J2007-068

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Lattice grids are new-type materials with high specificstiffness and specific strength. The topologies of the 2D periodic lattices are analyzed together with their manufacturing methods. Equivalent continuummethods to obtain effective stiffness, strength and yield surfaces arediscussed, including the micropolar elastic theory of the latticestructures. The size effect and influence of soft or rigid inclusions are analyzed. The fracture mechanics analysis on the cellulargrids shows that the triangular and hexagonal grids are flawsensitive, while the Kagome lattices are damage tolerant. The latticegrids may be classified into grid structures,grid stiffened structures and grid sandwich structures. The failure modes,the optimzation principles and the experiment results are discussed indetails. The recent work of the authors on carbon fiber reinforced latticematerials are also introduced.

REVIEW ON EXPERIMENTAL METHODS AND FRACTURE MODELS FOR BI-MATERIAL INTERFACES

2008, 38(1): 53-61. doi: 10.6052/1000-0992-2008-1-J2006-097

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With increasing use of advanced composite and hybridmaterials in engineering, the analysis of fracture mechanismsof interface bond between conventional materials and composites (e.g.,fracture of concrete-composite or wood-composite interface) becomes aninteresting topic. In this paper, the recent development of fracture models ofbi-material interfaces is reviewed. The crack tip fields at a bi-materialinterface are first disussed, followed by a comparison of differenttheories for interface fracture analysis, including (1) Classicalbeam/plate theory and rigid joint model, (2) Bi-layer shear deformable beamtheory and semi-rigid joint model, (3) Bi-layer interface deformable modeland flexible joint model, (4) Multi-sub-layer shear deformable beam theoryand multi-sub-layer joint model, (5) Beam on elastic foundation model, and(6) Non-linear cohesive model. The analytical models, common fracturespecimen configurations, and experimental techniques for mode I, mode II andmixed mode fracture of adhesively bonded interface are compared. Anoverview of researches on fracture of concrete-FRP bonded interfaces ispresented, and some recommendations are made and future researchdirections for fracture of bi-material interface are pointed out.

ADVANCES IN THE STUDY OF COMPRESSIBLE MIXING LAYER IN RECENT TEN YEARS

2008, 38(1): 62-76. doi: 10.6052/1000-0992-2008-1-J2007-037

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This paper reviews the studies on compressible mixing layerduring the past decade. These researches may beclassified into stability analysis, laboratory experiments and numericalsimulations, with a focus on the effectsof compressibility on other properties of mixing layer, including the growthrate, unstable modes, flow field structure, mean velocities and fluctuatevelocities, and the scalar mixing. The three aspects of researches complement eachother and give abundant information to understand the compressiblemixing layer. The researches cover an important part of the study onturbulent mechanism, and are essential for successful applicationsof mixing layer in technical areas.

ON UNSTEADY AERODYNAMIC MODELING BASED ON CFD TECHNIQUE AND ITS APPLICATIONS ON AEROELASTIC ANALYSIS

2008, 38(1): 77-86. doi: 10.6052/1000-0992-2008-1-J2006-158

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CFD technique can be used to study aeroelasticproblems with aerodynamic non-linearity. The disadvantage of the CFD basedaeroelastic direct simulation is the high computational cost which preventsit to be used for qualitative analysis or parametric design. CFD based ROM(reduced order model) technique can solve the contradictionbetween computational efficiency and computational quality, and thecontradiction between complexity and convenience for analysis and design. Areview on two kinds of ROM and harmonic balance for nonlinearunsteady aerodynamics is made in this paper. Recent aeroelastic researches based onthese methods are summarized. The advantages of these methods arecompared and the future development is discussed.

REVIEW ON GRANULAR FLOW DYNAMICS AND ITS DISCRETE ELEMENT METHOD

2008, 38(1): 87-100. doi: 10.6052/1000-0992-2008-1-J2006-180

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Granular flow concerns large assemblages of individual solids, andis fundamentally different from any other type of flow. Common granularflows in nature, such as debris flow, landslides and chutes, are denselypacked with solid fractions, over 50{\%} by volume. The interparticlecontact forces are found not evenly distributed throughout the granularmaterial, but are concentrated in force chains supporting the bulk ofinternal compressive stress. Therefore, contact mechanics of particles anddynamic evolution of force chains have a significant effect on the rheologicalproperties of granular flows. In this review paper, we first introduceHertzian law and Mindlin-Deresiewicz theory for normal and tangentialcontact forces between non-adhesion particles. We then discuss thenew granular flowmap proposed by Campbell (2002; 2005; 2006), based on therelative importance of Bagnold's inertial stress to the elastic stress offorce chains. The limitations of Mohr--Coulomb theory and kinetics forquasistatic and the rapid-flow regimes, respectively, are also discussed. Forintermediate flow regimes, no appropriate theory is proposed so far. Over 30years' development, discrete element methods (DEM), a package of numericaltechniques to model granular materials, may well be used to study granularflows. The potential value of DEM is the ability to obtain information that isnormally inaccessible and to perform rigorous parametric studies. Thesoft-sphere model, one of the widely used DEM models in engineeringapplications, simplifies sophisticated contact mechanics and deformationdetails into an easy-to-use contact model. However, one of tricky problemsarising from this simplification is the calibration of introducedparameters with realistic physical quantities. The hard-sphere model isfurther simplified and has very limited applications so far. We concludethat only the DEM based on rigorous contact mechanics on individualparticles could help the fundamental study on granular flows, such asinternal force chains properties related with constitutive relation, and eventuallybe applicable in natural process.

ENVIRONMENTAL FLUID DYNAMICS IN SEMI-HERMETIC AND HERMETIC VENTILATED SYSTEMS

2008, 38(1): 101-111. doi: 10.6052/1000-0992-2008-1-J2006-167

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Environmental fluid dynamics in semi-hermetic and hermeticventilated systems, including air motion, temperature and moisturedistribution and contaminant condensation, is a widely concernedsubject because of its applications in monitoring indoor airquality, designing ventilation system and avoiding vaporcondensation. This paper reviews the relatedtheoretical, numerical and experimental researches for high ventilation efficiency, low energy costs and moreair comfort in practice. They involve both semi-hermeticsystems (room, building and city) and hermetic systems (car, subway,plane, submarine and manned space capsule). The current theoreticalmodels were developed from the basic plume theory with a singlesource to complicated turbulent fountain models with buoyancyfluxes from the plume sources and momentum fluxes from the fountainsources. However, the theoretical analysis is incapable of dealingwith practical problems in situations such as of multiple ventilations andmultiple geometric structures, so most engineering applications tendto rely on experiments and numerical simulations. It is worthmentioning that researches on environmental fluid dynamics in mannedspace capsules, although just in a beginning stage, can use the matured researchstrategies and techniques in related semi-hermetic and hermeticsystems.

Rethinking on how research work of mechanics should be conducted

2008, 38(1): 112-113. doi: 10.6052/1000-0992-2008-1-J2007-098

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2008, 38(1): 114-116. doi: 10.6052/1000-0992-2008-1-J2007-161

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THE THIRD NATIONAL WORKSHOP ON ENVIRONMENTAL MECHANICS

2008, 38(1): 117-120. doi: 10.6052/1000-0992-2008-1-J2007-160

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2008, 38(1): 121-127. doi: 10.6052/1000-0992-2008-1-J2007-156

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2008, 38(1): 128-129. doi: 10.6052/1000-0992-2008-1-J2007-130

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L.X. Zhou Lixing Zhou

2008, 38(1): 131-131. doi: 10.6052/1000-0992-2008-1-J2007-124

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2008, 38(1): 132-136. doi: 10.6052/1000-0992-2008-1-J2008-011

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