外文翻譯--用有限元分析法計(jì)算壓力容器的塑性崩潰負(fù)載（英文）

1、Liu et al. / J Zhejiang Univ Sci A 2008 9(7):900-906 900Calculations of plastic collapse load of pressure vessel using FEA* Peng-fei LIU?, Jin-yang ZHENG??, Li MA, Cun-jian MIAO, Lin-lin WU (Institute of Chemical Machi

2、nery and Process Equipment, Zhejiang University, Hangzhou 310027, China) ?E-mail: pfliu1980@yahoo.com; jyzh@zju.edu.cn Received Jan. 9, 2008; revision accepted Apr. 2, 2008 Abstract: This paper proposes a theoretical

3、 method using finite element analysis (FEA) to calculate the plastic collapse loads of pressure vessels under internal pressure, and compares the analytical methods according to three criteria stated in the ASME Boiler

4、 Pressure Vessel Code. First, a finite element technique using the arc-length algorithm and the restart analysis is developed to conduct the plastic collapse analysis of vessels, which includes the material and geometry

5、 non-linear properties of vessels. Second, as the mechanical properties of vessels are assumed to be elastic-perfectly plastic, the limit load analysis is performed by em- ploying the Newton-Raphson algorithm, while the

6、 limit pressure of vessels is obtained by the twice-elastic-slope method and the tangent intersection method respectively to avoid excessive deformation. Finally, the elastic stress analysis under working pressure is c

7、onducted and the stress strength of vessels is checked by sorting the stress results. The results are compared with those obtained by experiments and other existing models. This work provides a reference for the selecti

8、on of the failure criteria and the calculation of the plastic collapse load. Key words: Plastic collapse load, Pressure vessel, Finite element analysis (FEA), Design by analysis (DBA) doi:10.1631/jzus.A0820023

9、 Document code: A CLC number: TH12 INTRODUCTION The objective of pressure vessel design by analysis (DBA) is to prevent various possible failures and to ensure safe operation of vessels.

10、 This is prac- tically realized by limiting the stresses, strains and design loads of vessels within the allowable values after the failure modes of vessels are determined. However, under excessive static internal pre

11、ssure, the vessels may experience gross plastic deformation and eventually collapse. Currently, several international codes of pre-venting the plastic instability in DBA have been de- veloped, such as the ASME (2007) c

12、ode and the EN 13445-3 (2002) code. Among them, the ASME code proposes three criteria to prevent the plastic instabil- ity of vessels: the elastic stress analysis criterion, the limit load analysis criterion and the e

13、lastic-plastic stress analysis criterion. In the elastic stress analysis, the calculated stresses are classified into the primary, secondary and peak stresses, which are all limited by introducing the allowable values

14、. The limit load analysis assumes the elastic-perfectly plastic material property and small deformation of vessels, but no gross plastic deformation. The twice-elastic-slope method proposed by the ASME (2007) code an

15、d the tangent intersection method proposed by the EN 13445-3 (2002) code are employed to determine the limit loads of vessels based on the derived pres- sure-deformation parameter curves. It is not easy to select a s

16、uitable deformation parameter especially when multiple loads are acting on the vessels. In contrast, the elastic-plastic stress analysis which di- rectly takes into account the actual material and ge- ometry nonlinear

17、properties of vessels, may result in gross plastic deformations before structural plastic collapse. In this case, the mechanical behaviors of vessels and the load carrying capacity of vessels in the elastic-plastic s

18、tress analysis are more practical than those in other two methods. Therefore, it is important Journal of Zhejiang University SCIENCE A ISSN 1673-565X (Print); ISSN 1862-1775 (Online) www.zju.edu.cn/jzus; www.springerlin

19、k.com E-mail: jzus@zju.edu.cn ? Corresponding author * Project (Nos. 2006BAK04A02-02 and 2006BAK02B02-08) sup-ported by the National Key Technology R (2) ΔY=0 at the bottom head face of the cylinder; (3) ΔX=0 at any n

20、ode to eliminate the rigid body displacement of the structure. The material 16MnR is considered to be iso-tropic and elastic-plastic. Its mechanical properties are listed in Table 1 (Wang et al., 2000). Elastic-plastic

21、stress analysis According to the Remberg-Osgood power hardening model, the mechanical properties of the material 16MnR can be expressed as (Wang et al., 2000) ε/ε0=σ/σ0+(σ/σ0)n, (1) where ε0=

22、1.643×10?3, σ0=300 MPa and n=9 are the characteristic strain, stress and the hardening expo- nent, respectively. In the finite element preprocessing, the true stress-strain curve after plastic deformation is fitted

23、 by importing 50 discrete stress-strain points to the ANSYS-APDL software. The constitutive relation- ship of material is shown in Fig.3. The elastic-plastic stress analysis of the structure under internal pressure can

24、 be conducted using the Newton-Raphson iterative algorithm. However, for the sudden plastic collapse of the structure, this method cannot further track the load path and be- comes invalid because the integrated structu

25、ral stiff- ness matrices of the structure at the plastic collapse point are singular, as shown in Fig.4. To solve this problem, the arc-length algorithm is adopted to track the nonlinear post-necking path and to calcul

26、ate the plastic collapse load of the structure, as shown in Fig.5. This method is originally proposed by Wempner (1971) and Riks (1979), and further improved by Ramm (1981) and Crisfield (1983). To handle zero and ne

27、gative tangent stiff- nesses, the arc-length algorithm multiplies the in- cremental load by a load factor λ, where λ is between ?1 and 1. This extra unknown variable λ alters the finite element equilibrium equation to K

28、Tu=λFa?Fnr, where Fa is the external force and Fnr is the internal non-balanceable force. To deal with this, the arc-length method imposes another constraint, which is stated as 2 2 , n u R λ Δ + =(2) where Δu is the

29、 displacement increment and R is the arc-length radius. Table 1 Mechanical properties of 16MnR Parameter Value Young’s modulus (MPa) 2.05×105 Poisson’s ratio 0.3 Yielding strength (MPa) 350 Tensile strength 5

30、30 Failure strain 0.248 F u Stiffness matrix is singular Fig.4 Newton-Raphson iterative algorithm λ λn λi 1 i+1 i Δλ Δui″Δui′ Δunun (converged solution at substep n) u (n+1) converged solution Spherical arc at subste