应用数学和力学

2003 Vol. 24, No. 2

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Constitutive Relation of Unsaturated Soil by Use of the Mixture Theory(Ⅰ)-Nonlinear Constitutive Equations and Field Equations

HUANG Yi, ZHANG Yin-ke

2003, 24(2): 111-123.

Abstract(2554) PDF(1097)

Abstract:
The nonlinear constitutive equations and field equations of unsaturated soils were constructed on the basis of mixture theory. The soils were treated as the mixture composed of three constituents. First, from the researches of soil mechanics, some basic assumptions about the unsaturated soil mixture were made, and the entropy inequality of unsaturated soil mixture was derived. Then, with the common method usually used to deal with the constitutive problems in mixture theory, the nonlinear constitutive equations were obtained. Finally, putting the constitutive equations of constituents into the balance equations of momentum, the nonlinear field equations of constituents were set up. The balance equation of energy of unsaturated soil was also given, and thus the complete equations for solving the thermodynamic process of unsaturated soil was formed.

Constitutive Relation of Unsaturated Soil by Use of the Mixture Theory(Ⅰ)-Nonlinear Constitutive Equations and Field Equations

HUANG Yi, ZHANG Yin-ke

2003, 24(2): 124-137.

Abstract(2272) PDF(763)

Abstract:
The linear constitutive equations and field equations of unsaturated soils were obtained through linearizing the nonlinear equations given in the first part of this work. The linear equations were expressed in the forms similar to Biot's equations for saturated porous media. The Darcy's laws of unsaturated soil were proved. It is shown that Biot's equations of saturated porous media are the simplification of the theory. All these illustrate that constructing constitutive relation of unsaturated soil on the base of mixture theory is rational.

Analytical Solutions of Thermal Stress Distribution in Plastic Encapsulated Integrated Circuit Packages

LIU Yu-lan, WANG Biao, WANG Dian-fu

2003, 24(2): 138-145.

Abstract(2454) PDF(653)

Abstract:
Due to the mismatch in the coefficients of thermal expansion of slicon chip and the surrounding plastic encapsulation materials, the induced thermal stress is the main cause for die and encapsulant rupture. The corner geometry is simplified as the semi-infinite wedge. Then the two-dimensional thermal stress distribution around the corner was obtained explicitly. Based on the stress calculation, the strain energy density factor criterion is used to evaluate the strength of the structure, which can not only give the critical condition for the stresses, but also determine the direction of fracture initiation around the corner.

A Class of Nonlinear Boundary Value Problems for the Sceond-Order E₂ Class Elliptic Systems in General Form

LI Ming-zhong, XU Ding-hua

2003, 24(2): 146-162.

Abstract(2395) PDF(722)

Abstract:
A class of nonlinear boundary value problems(BVP) for the second-order E₂ class elliptic systems in general form is discussed. By introducing a kind of transformation, this kind of BVP is reduced to a class of generalized nonlinear Riemann-Hilbert BVP. And then some singular integral operators are introduced to establish the equivalent nonlinear singular integral equations. The solvability is proved under some suitable hypotheses by means of the properties of singular integral operators and the function theoretic methods.

Active Control of the Piezoelastic Laminated Cylindrical Shell’s Vibration Under Hydrostatic Pressure

LI Hong-yun, LIN Qi-yong, LIU Zheng-xing, WANG Chao

2003, 24(2): 163-174.

Abstract(2211) PDF(841)

Abstract:
The control of the piezoelastic laminated cylindrical shell. s vibration under hydrostatic pressure was discussed. From Hamilton. s principle nonlinear dynamic equations of the piezoelastic laminated cylindrical shell were derived. Based on which, the dynamic equations of a closed piezoelastic cylindrical shell under hydrostatic pressure are obtained. An analytical solution was presented for the case of vibration of a simply supported piezoelastic laminated cylindrical shell under hydrostatic pressure. Using veloctity feedback control, a model for active vibration control of the laminated cylindrical shell with piezoelastic sensor/actuator is established. Numerical results show that, the static deflection of the cylindrical shell can be changed when voltages with suitable value and direction are applied on the piezoelectric layers. For the dynamic response problem of the system, the larger the gain is, the more the vibration of the system is suppressed in the vicinity of the resonant zone. This presents a potential way to actively reduce the harmful effect of the resonance on the system and verify the feasibility of the active vibration control model.

UGD Property of Musielak-Orlicz Sequence Spaces

WANG Ting-fu, JI Dong-hai, CAO Lian-ying

2003, 24(2): 175-184.

Abstract(1806) PDF(600)

Abstract:
By the properties of the Musielak-Orlicz funcitons. sequence, the necessary and sufficient condition for uniform Gateaux differential(UGD) property of Musielak-Orlicz sequence spacesequipped with the Luxemburg norm and a criterion for weakly uniform rotundity of Musielak-Orlicz sequence space with Orlicz nor mare given.

Asymptotic Dynamic Solution to the Mode Ⅰ Propagating Crack-Tip Field in Elastic-Viscoplastic Material

LI Fan-chun

2003, 24(2): 185-191.

Abstract(2162) PDF(431)

Abstract:
A new elastic-viscoplastic mode was proposed to analyze the stress and strain fields surrounding the tip of a propagating mode cracks. A proper displacement pattern was suggested and asymptotic equations were derived, and numerical solutions were illustrated. The analysis and calculation show that the crack-tip field is of logarithmic singularity for smaller viscosity, however no solution exits for large viscosity. By a careful analysis and comparison, it is found that the present results retain all merits of those given by GAO Yu-chen, while removing existing problems.

The Constitutive Equations for Mixed Hardening Orthotropic Material

LIU Teng-xi, HUANG Shi-qing, FU Yi-ming

2003, 24(2): 192-196.

Abstract(3082) PDF(1154)

Abstract:
A dimensionless stress yield criterion is proposed to describe the mixed hardening of orthotropic material, including kinematic hardening and proportional hardening, and the associated plastic flow law is derived. The generalized effective stress-strain formulae can be obtained correspondingly based on the experimental stress-strain curves in various simple stress states. The initial plastic anisotropy is influenced by the elastic anisotropy. The yield creterion can be reduced to Huber-Mises Criterion for isotropic materials and associated constitutive equations can be degenerated into PrandtlReuss Equations.

Epsilon-Algorithm and Eta-Algorithm of Generalized Inverse Function-Valued Padé Approximants Using for Solution of Integral Equations

LI Chun-jing, GU Chuan-qing

2003, 24(2): 197-204.

Abstract(2195) PDF(693)

Abstract:
Two efficient recursive algorithms epsilon-algorithm and eta-algorithm are introduced to compute the generalized inverse function-valued Pad approximants. The approximants were used to accelerate the convergence of the power series with function-valued coefficients and to estimate characteristic value of the integral equations. Famous Wynn identification of the Padé approximants is also established by means of the connection of two algorithms.

An Analysis Model of Pulsatile Blood Flow in Arteries

LIU Zhao-rong, XU Gang, CHEN Yong, TENG Zhong-zhao, QIN Kai-rong

2003, 24(2): 205-214.

Abstract(2380) PDF(958)

Abstract:
Blood flow in artery was treated as the flow under equilibrium state(the steady flow under mean pressure) combined with the periodically small pulsatile flow. Using vascular strain energy function advanced by Fung, the vascular stress-strain relationship under equilibrium state was analyzed and the circumferential and axial elastic moduli were deduced that are expressed while the arterial strains around the equilibrium state are relatively small, so that the equations of vessel wall motion under the pulsatile pressure could be established here. Through solving both the vessel equations and the linear Navier-Stokes equations, the analytic expressions of the blood flow velocities and the vascular displacements were obtained. The influence of the difference between vascular circumferential and axial elasticities on pulsatile blood flow and vascular motion was discussed in details.

A Semi-Analysis Method of Differential Equations With Variable Coefficients Under Complicated Boundary Conditions

LI Ming-an, WANG Zhong-min, GUO Zhi-yong]

2003, 24(2): 215-220.

Abstract(2310) PDF(914)

Abstract:
Based on a method of finite element model and combined with matrix theory, a method for solving differential equations with variable coefficients is proposed. With that method, it is easy to deal with the differential equations with variable coefficients. On most occasions, due to the non-uniformity nature, non-linearity property can cause the kind equations. Using that model, the satisfactory valuable results with only a few units can be obtained.