应用数学和力学

2015 Vol. 36, No. 3

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Optimal Design of Thin Solid Elastic Plates Under Thermal Load

NI Xiao-qin, CHENG Geng-dong

2015, 36(3): 233-241. doi: 10.3879/j.issn.1000-0887.2015.03.001

Abstract(1106) PDF(1090)

Abstract:
Plates and shells constitute a large family of widely used structural elements. Under the action of thermal load, if the thermal expansion is restricted, membrane forces and bending moments will occur within the plate and shell structures and lead to large deformation which seriously affected normal service. Due to the particularity of thermal load, uniform increase of the plate or shell thickness can hardly reduce the thermal deformation and thermal stress effectively, and special experience and knowledge are required in thermal structural design. Thickness distribution optimization of the thin elastic plate structure with given material volume under thermal load was studied and aimed at reduction of thermal deformation. For the thickness distribution of the plate with given material volume, mathematical formulation of the optimization problem focused on minimum structural deformation energy was established. According to the formulation and with the variational method, the optimality criteria and the iterative scheme for modification of the thickness distribution were derived. And this optimization algorithm was implemented through secondary development in the commercial finite element programs. Results of the numerical examples show that, the presented method greatly reduces the thermal deformation of thin elastic plate structures through modification of the thickness distribution, and makes an effective optimization method for thermal structures.

A Multi-Symplectic Method for Dynamic Responses of Incompressible Saturated Poroelastic Rods

LIU Xue-mei, DENG Zi-chen, HU Wei-peng

2015, 36(3): 242-251. doi: 10.3879/j.issn.1000-0887.2015.03.002

Abstract(960) PDF(816)

Abstract:
Dynamic responses of incompressible saturated poroelastic rods were investigated. Based on the theory of porous media, the 1D axial vibration equation for a fluid saturated elastic porous rod was established, in which the saturated porous material was modeled as a 2-phase system composed of an incompressible solid phase and an incompressible fluid phase. Then a 1st-order multi-symplectic form for the axial vibration equation and several local conservation laws for the saturated poroelastic rod were derived with the multi-symplectic method. Moreover, the midpoint Box multi-symplectic scheme for the axial vibration equation, and the discrete schemes for the local energy conservation law and local momentum conservation law were constructed with the midpoint method. Finally, the axial vibration process of the incompressible saturated poroelastic rod was simulated numerically and numerical errors of the local energy conservation law and local momentum conservation law were also discussed by means of the numerical results of each time step and each time-space step, respectively. The results show that the proposed multi-symplectic scheme has advantages of high accuracy, long-time numerical stability and good conservation properties, and this method provides a new way to solve the dynamic responses of saturated porous media.

Mechanical Behaviors of the FCI With Various Geometric Characteristics in Multi-Physics Fields

LI Ming-jian, CHEN Long, NI Ming-jiu, ZHANG Nian-mei

2015, 36(3): 252-261. doi: 10.3879/j.issn.1000-0887.2015.03.003

Abstract(985) PDF(795)

Abstract:
The flow channel insert (FCI) is an indispensable component in the ITER. It serves as the thermal and electric insulator in the blanket module. The mechanical behaviors of the FCI were investigated under the coupling effects of magneto-thermo-fluid-mechanical fields. Numerical investigations based on the finite volume method and finite element method were applied. The velocity profiles, temperature distributions and structural stress states were analyzed. Influences by the magnetic field and geometric characteristics of the FCI on the blanket module were investigated. Results show that, a stronger magnetic field causes lower first-wall (FW) temperature and FCI thermal stresses despite leading to the MHD effects, a thicker FCI yields lower FW temperature yet higher FCI temperature gradient and thermal stresses, and a wider gap leads to lower FW temperature yet higher Mises stresses in the FCI.

Buckling of Shallow Spherical Shells Under Uniform Pressure in Uniform Temperature Field

ZHAO Wei-dong, YANG Ya-ping

2015, 36(3): 262-273. doi: 10.3879/j.issn.1000-0887.2015.03.004

Abstract(824) PDF(1002)

Abstract:
According to the geometrical nonlinear theory for shallow shells, the displacementtype geometrical nonlinear governing equations for shallow spherical shells under uniform pressure in uniform temperature field were derived. With the shooting method, the numerical results of axisymmetric bending and buckling of the shallow spherical shell in the clamped boundary condition were obtained. The effects of various shell geometrical parameters on the equilibrium paths and the critical loads were discussed. The critical shell geometrical parameter was defined. And it is found that both the upper and lower critical loads increase with the geometrical parameter in the range beyond its critical value. The effects of different values of the uniform temperature field on the upper and lower critical loads, the critical geometrical parameter, and the equilibrium configurations were investigated under a given geometrical parameter. Rise of the uniform temperature brings obvious increase of the upper critical load and slight decrease of the lower critical load. Moreover, change of the uniform temperature influences the critical shell geometrical parameter a lot.

Fluid-Solid-Heat Coupling Study on Liquid Film Seal for High Temperature Oil Pumps

YANG Dan-dan, HAO Mu-ming, ZHANG Yuan, ZHANG Da-hai, ZHUANG Yuan, WANG Xuan-ying

2015, 36(3): 274-284. doi: 10.3879/j.issn.1000-0887.2015.03.005

Abstract(1019) PDF(1197)

Abstract:
A periodical model for rotor-stator rings was constructed with the meshing software, and the 3D force coupling and force-heat coupling behaviors of the rotor-stator system were computed by means of ANSYS Workbench 15.0. The influences of the force coupling and force-heat coupling on the ring end face deformation were investigated. The operation parameters (speed, pressure difference) affecting the end face deformation were discussed and the stresses caused by the force-heat coupling were analyzed. It is concluded that the circumferential wavy deformation and radial tapering deformation generated by the force coupling are beneficial to stability of the interstitial fluid, the deformation generated by the thermal load plays a major role in the total deformation by the force-heat coupling, and the rotation rate has noticeable influence on the deformation by the force-heat coupling.

Solving of the Structural Fuzzy Reliability Analysis Method With Universal Grey Numbers

LIU Jie, QING Qi-xiang, ZHANG Qing-chun, CHEN Xiao-yue

2015, 36(3): 285-293. doi: 10.3879/j.issn.1000-0887.2015.03.006

Abstract(1225) PDF(969)

Abstract:
To overcome the defects in the existing interval solving of the structural fuzzy reliability analysis method, a new method was proposed. Universal grey numbers were used to describe the basic uncertain parameters related to the probability distributions of the variables, and then these numbers were introduced into analysis of the fuzzy reliability of structures, to give more accurate results. The numerical example shows that the proposed method gets narrower intervals of structural reliability, and achieves more accurate reliability calculation results with less input information. What’s more, in comparison with the traditional fuzzy reliability calculation procedures, the proposed method provides more available and more accurate information about the safety degree of the related structure.

Connectional Matrix-Based Combination Evaluation Method for Surrounding Rock Stability

WANG Ming-wu, WEI Dong-fang, ZHOU Xin-wei, WANG Peng-cheng

2015, 36(3): 294-302. doi: 10.3879/j.issn.1000-0887.2015.03.007

Abstract(774) PDF(794)

Abstract:
Evaluation of surrounding rock stability is a complicated system problem involving various uncertain factors. To overcome the drawbacks of conventional evaluation methods based on single-type information, a new combination evaluation method based on set pair analysis was proposed. This method made full use of available information sources from the different conventional methods while avoiding the most erroneous evaluation. First, the problem was treated with the single-type evaluation methods. Then, the set pair consisting of double evaluation results was analyzed on the identical-discrepancy-contrary principle to establish a connectional matrix. And the weights of the realted single-type evaluation methods in the comprehensive model were determined respectively through the connectional matrix. Finally the surrounding rock stability level was evaluated with the linear combination method. The results of the application case show that the proposed model is effective and feasible in improving the prediction accuracy through coupling the advantages of the related conventional evaluation methods. This method makes a good reference for other similar evaluation problems.

On the Construction of Stiffness Matrices With 3 Vector Pairs for Beam Vibration Systems

ZHOU Shuo, Lü Xiao-huan, WANG Xiao-xue

2015, 36(3): 303-314. doi: 10.3879/j.issn.1000-0887.2015.03.008

Abstract(1189) PDF(810)

Abstract:
The stiffness matrix of the discrete vibrating beam model is a real symmetric 5-diagonal matrix, so the inverse problem of the vibrating beam is substantially an inverse eigenvalue problem of the real symmetric 5-diagonal matrix. The existence and uniqueness conditions for the solution to the inverse problem of the real symmetric 5-diagonal matrix vector pair were given by means of the vector pairs and the Moore-Penrose generalized inverse, and the existence and uniqueness conditions for the solution to the inverse problem of the bi-symmetric 5-diagonal matrix vector pair were discussed in combination with the partitioned matrices. Then the inverse eigenvalue problem of the real symmetric 5-diagonal matrix, of which the sub-diagonal elements were negative and the rest elements were positive, was calculated. Since the data required for the construction of discrete beam models are available through measurements, the presented method is well suited to modal analysis, or analysis and design of system structures. Furthermore, the related numerical algorithms and numerical experiments illustrate the effectiveness of the method.

Travelling Wave Solution to a Class of Generalized Nonlinear Strong-Damp Disturbed Evolution Equations

FENG Yi-hu, SHI Lan-fang, WANG Wei-gang, MO Jia-qi

2015, 36(3): 315-324. doi: 10.3879/j.issn.1000-0887.2015.03.009

Abstract(1120) PDF(917)

Abstract:
A class of generalized nonlinear strong-damp disturbed evolution differential equations were studied, which widely appeared in the fields of mathematics, mechanics and physics etc.. Firstly, a travelling wave transformation was introduced to convert the related problem of partial differential equations to one of travelling wave equations, with the exact solution to the original typical problem obtained. Then the small parameter method was used and the stretched variables introduced to construct the asymptotic solution. Finally, the existence, high accuracy and uniform validity of the asymptotic travelling wave solution to the original generalized nonlinear strong-damp disturbed evolution equation for the initial-value problem were proved with the fixed point theory for functional analysis. The presented travelling wave asymptotic solution is an analytic expansion, therefore, it is continuously open to analytic operations, which reject the solutions given by those pure numerical methods.

A Note on Some New Characteristics of D-Semi-Preinvexity

TANG Li-ping, YANG Xin-min

2015, 36(3): 325-331. doi: 10.3879/j.issn.1000-0887.2015.03.010

Abstract(935) PDF(798)

Abstract:
Some new properties of semi-preinvexity in the sense of cones were studied. Firstly, Example 4 in the paper of PENG Zai-yun, etc.(PENG Zai-yun, LI Ke-ke, TANG Ping, HUANG Ying-quan. Characterizations and criterions of D-semiprequasi-invex mappings[J].Journal of Chongqing Normal University(Natural Science),2014,31( 5 ):18-25.) was modified to satisfy condition E. Then, an important property of condition E₁ was obtained. Based on this property and the results of density, two characterizations of D-semi-preinvexity were established by means of D-semi-strict semi-prequasiinvexity and D-strict semi-prequasiinvexity, respectivley. In the end,D-semi-preinvexity was characterized with D-semi-prequasiinvexity.

Quadruple Coincidence Point Theorems for Mixed g-Monotone Mappings in Partially Ordered Metric Spaces and Their Applications

XU Wen-qing, ZHU Chuan-xi, WU Zhao-qi

2015, 36(3): 332-342. doi: 10.3879/j.issn.1000-0887.2015.03.011

Abstract(898) PDF(741)

Abstract:
The concepts of α-admissible mappings and compatible mappings for a pair of mappings F:X⁴→X and g:X→X in partially ordered metric spaces were constructed. Based on this, with the iterative method, existence and uniqueness of the quadruple coincidence points for the α-admissible and compatible mappings satisfying the mixed g-monotone properties under the α-ψ-contractive conditions in the partially ordered complete metric spaces were studied, and some new theorems were established. Finally, 2 examples were presented as applications of the main theorems. The results show that the work generalizes and improves several fixed point theorems and coincidence point theorems in the recent corresponding literatures.