外文翻譯--大體積混凝土溫度和徐變的數(shù)值實(shí)現(xiàn)（原文）

1、* Corresponding author.Finite Elements in Analysis and Design 37 (2001) 97}106Numerical implementation of temperature and creep in mass concreteYong Wu, Ronaldo Luna*Department of Civil Engineering, University of Missour

2、i-Rolla, 1870 Miner Circle, Rolla, MO 65409, USAAbstractMass concrete generates internal heat during the hydration period that occurs soon after casting. Added to these internal heat changes are the environmental conditi

3、ons that the structure is subjected to during its design life. These thermal changes in the material a!ect the elastic and creep properties of the material, and in turn, the stress “elds within the structure. The numeric

4、al implementation of these factors is illustrated in a three-dimensional “nite element program that simulates the construction process of mass. The mathemat- ical formulation, the numerical implementation and other imple

5、mentation details are presented herein. The temperature and stress variation of a concrete block was analyzed and results show that temperature plays an important role in concrete structures. ? 2001 Elsevier Science B.V.

6、 All rights reserved.Keywords: FEM; Mass concrete; Thermal stresses; Creep; Numerical method1. IntroductionThe design and construction of mass concrete structures involves solving the problem of thermal stresses and temp

7、erature control. The material temperature changes due to two factors: (1) the internal hydration of concrete and (2) the environmental boundary conditions. Temperature not only in#uences the elastic modulus and creep pro

8、perties of concrete, but it also produces thermal stresses. The temperature increase accelerates the initial elastic modulus of concrete. The creep rate is also increased with higher temperature and the creep strain is e

9、nlarged [1,2]. Therefore, the elastic modulus and creep variations at di!erent locations within the mass concrete structures are all a function of temperature and which in turn is a function of time. This requires extend

10、ing the analysis into another dimension, time. This spatio-temporal problem requires the modi“cation of material properties with time, and if construction is being simulated, changes in gravity dead load0168-874X/01/$- s

11、ee front matter ? 2001 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 8 - 8 7 4 X ( 0 0 ) 0 0 0 2 2 - 6On boundary C?, convective-type condition is applied. This condition is when there are changes in temperatur

12、e along that boundary:?? ?¹?x l?#?? ?¹?y l?#?? ?¹?z l?“!?(¹!¹?), (5)where ¹ is the transient temperature, ? is the adiabatic temperature rise of concrete, ¹? is the initial temperature,

13、 n is the outer normal of the boundary, ??, ??, ?? are the thermal conductivities for each direction, ? is the surface exothermic coe$cient, ¹? is the temperature of the bounding #uid, and l?, l?, l? are direction c

14、osines of the external normal to the boundary. The above problem can be solved in 3D using the “nite element method, the equations for “nite element method are listed as follows:?H# 2?tP??¹??#?H! 2?tP??¹?????#?

15、Q?????#?Q??“0, (6)whereH??“??h? ??“?? ????? ?a? ?N? ?x?N? ?x #a? ?N? ?y?N? ?y #a? ?N? ?z?N? ?z ? dx dy dz,P??“??p? ??“?? ?????N?N? dx dy dz,Q??“??q? ?“???!????????t N? dx dy dz!????? M ¹?N? ds#?????? M N?[N?N?2] ds?

16、?¹? ¹? ???.Therefore, if the temperature at time t!?t is known, then the temperature at time t can be calculated, since the initial temperature is known, the temperature at any time can be calculated.3. Creep s

17、tress with temperature e4ectsIn creep analysis, the most widely used models are the CEB-FIP Model [3]; the American Concrete Institute (ACI) Model [4]; the Bazant and Panula's (BP) Model [5] and the ExponentialY. Wu,