本文應用移動參考構架法（Convected Material Frame Approach, CMF）並改變分析流程中的組成律，文中材料之應力應變關係以非線彈性函數表示，使之可以針對不同的材料特性進行非線彈性結構的暫態、擬靜態分析及受反覆載重下的力學行為進行探討，本研究亦模擬結構於高溫火場環境的力學行為，本文並應用MPI (message passing interface)進行平行計算之研究。其目的在以叢集技術為架構的平行電腦上，探討平行計算的可行性與評估其效能，進而推廣平行處理的高效能計算環境。

移動參考構架法在分析的方法上是源於傳統的顯性有限元素法並將之改良而成。本方法將求解的過程離散化，先針對結構物將其化成有限個元素的集合，接著取前後分析時間點的變形差，求解桿件元素上的應力應變關係，再由此關係利用虛功原理求解結構動力平衡方程式，並輔以顯性時間積分法，以求解結構物在各歷時下的變位、速度與加速度；在分析時，利用微小時距間小變形的假設來模擬大變形問題，以避免數值運算上的問題。文中材料之應力應變關係以非線彈性函數表示，結果顯示移動參考構架法可合理地模擬結構大變形行為。

現行耐震設計大多利用非彈性行為以消散能量的概念去做設計。在高樓部份也廣泛應用鋼構斜撐來做為消散能量的方式。因此，對於鋼結構從受力到破壞的行為模式及鋼結構受反覆載重下的非彈性大變形分析為必要課題。本文利用移動參考構架法模擬結構的非幾何大變形行為並採用Dafalis-Popov Two-Surface Model (TSM)描述鋼構造受反覆荷重下的材料行為，結果顯示移動參考構架法可合理模擬鋼結構受反覆載重下的大變形行為，此外，本文亦採用澳洲規範描述高溫環境下之鋼結構的材料性質，結果顯示移動參考構架法可合理地模擬高溫環境下結構大變形行為。本研究並應用MPI進行不同平行電腦平台下平行計算效能分析，目的在以叢集技術為架構的平行電腦上，探討平行計算的可行性與評估其效能，平行計算的執行主要在國家高速電腦中心（NCHC）所提供的IBM SP2及電腦叢集（PC Clusters）執行並應用MPI進行不同平行電腦平台下平行計算效能分析結果顯示計算效能隨處理器數量增加而提升，並顯示移動參考構架法適用於進行平行處理且加速比隨處理器數量增加而提升。

This study presents the convected material frame approach to study the nonlinear behavior of inelastic frame structures. The convected material frame approach is a modification of the co-rotational approximation by incorporating an adaptive convected material frame in the basic definition of the displacement vector and strain tensor. In the formulation, each discrete element is associated with a local coordinate system that rotates and translates with the element. For each load increment, the corresponding strain-displacement and nodal force-stress relationships are defined in the updated local coordinates, and based on the updated element geometry. The rigid body motion and deformation displacements are decoupled for each increment. This modified approach incorporates the geometrical nonlinearities through the continuous updating of the material frame geometry. A generalized nonlinear function is used to derive the inelastic constitutive relation and the kinematic hardening is considered. The equation of motion is integrated by an explicit procedure and it involves only vector assemblage and vector storage in the analysis by assuming a lumped mass matrix of diagonal form.

Many features of the adopted approach are presented in this research. For the purpose of considering the gradual plastification through the cross section and along the member length, the Bauschinger effect, strain hardening and residual stresses produced during hysteretic plastic deformation, the convected material frame approach adopted the Dafalis-Popov two-surface model analyze the nonlinear cyclic plasticity behavior of the steel frames in this research. The structures subjected to horizontal triangular wave load, sine wave load, earthquake load, and horizontal harmonic wave load are studied. The numerical results show that the present approach is capable of simulating the nonlinear transient responses of frame structures.

The convected material frame approach is presented for analysis of nonlinear behavior of steel frames subjected to fire in the present study. The material and geometrical non-linearity as well as the uniform profile of temperature across section of frame members are taken into account. In recent years the rapid development of computer hardware environments with parallel processing capabilities has created new opportunities for revolutionizing engineering computing. The constant improvement of price/performance ratio of commodity computing hardware, coupled with the innovation of networking technology, has made cluster computing one of the most attractive computing architectures for both academic institutes and industrial organizations in the last several years. Therefore, this study investigates a parallel processing strategy for simulations of nonlinear behavior of inelastic structures. A parallel explicit finite element approach is employed to facilitate inelastic structural analysis more efficient. All the computation is carried out on the PC clusters in Linux and conventional parallel machine IBM SP2 at the National Center for High-Performance Computing (NCHC), Hsinchu, Taiwan. The message passing software package, MPI, is utilized as a parallel construct for data communication and message passing among processors.

Several numerical examples are demonstrated in close agreement with the solutions obtained by the ANSYS code. Numerical studies show that the proposed approach is capable of investigating large deflection of inelastic planar structures and providing an excellent numerical performance. The performance parallel computation studies indicate that this explicit algorithm is highly adaptive for parallel processing.

Agarwal, T.K, Storassli, O.O. and Nguyen, D.T. (1990).” A parallel-vector algorithm for rapid structural analysis on high-performance computer.” Proc. AIAA/ASME/ASCE/AHS 31st Structures,

Structural Dynamics and Materials Conference, Long Beach, CA, April 2-4, 662-672

Akl, K. and Morel, M. (1989).“ Eigensolution of finite element problems in a completely connected parallel architecture.” Proc. AIAA/ASME/ASCE/AHS 31st Structures, Structural Dynamics and Materials Conference, Mobile, AL, April 3-5, 2054-2063
ANSYS Release 5.5.1 (1998). ANSYS, Inc., Canonsburg, P. A., U. S. A

ASTM E119 (2000). Standard Test Methods for Fire Tests of Building Construction and Materials, American Society for Testing and Materials, United States

Bailey, C.G., Burgess, I.W. and Plank, R.J. (1996).” Analyses of the effects of cooling and fire spread on steel-framed buildings.” Fire Safety J., 26(4), 273-293

Bathe, K. J. (1982). Finite Element Procedures in Engineering Analysis, Prentice-Hall Inc.

Belytschko, T. and Hsieh, B. J. (1973). “Nonlinear transient finite element analysis with convected coordinates.” Int. J. Numer. Meth. Eng., 7, 255-271.

Belytschko, T. and Marchertas, A. H. (1974). “Nonlinear finite element method for plates and its application to dynamics response of reactor fuel subassemblies.”J. Pressure Vessel Tech., Trans. ASME, 96(4), 251-257.

Belytschko, T., Schwer, L., and Klein, M. J. (1977). “Large displacement, transient analysis of space frames.” Int. J. Numer. Meth. Eng., 11, 65-84.

Bresler, B. (1985)“Analytic prediction of structural response to fire,” Fire Safety J., 9, 103-117

Brockenbrough, R.L. (1970)” Theoretical stress and strains from heating curving.” J. Struct. Div., ASCE, 96, 1421-1444

Buch, M., Idesman, A., Niekamp, R. and Stein, E. (1999).” Finite elements in space and time for parallel computing of viscoelastic deformation.” Comput. Mech., 24(5), 386-395

Chaboche, J.L. and Rousselier, G. (1983). “On the plastic and viscoplastic constitutive equations - parts I and II,”J. Pressure Vessel Tech., Trans. ASME,105, 153-164.

Chiou, Y. J., Wang, Y. K., Hsiao, P. A., and Chen, Y.L. (2000).” Large displacement analysis of inelastic structures by convected material frame approach.” Struct. Engrg. Mech., 13(2), 135-154

CNS 12514 (2002). Methods of Fire Resistance Test for Structural Parts of Building, Bureau of Standards, Metrology and Inspection, Taipei, (in Chinese)

Crisfield, M. A. (1990). “ A consistent co-rotational formulation for non-linear, three dimensional beam elements.” Compt. Meth. Appl. Mech. Eng., 81, 131-150.

Dafalias, Y.F. and Popov, E.P. (1975) “A model of nonlinearly hardening materials for complex loading,” Acta Mechanica, Vol. 21, 173-192

Dafalias, Y.F. and Popov, E.P. (1976). “Plastic internal variables formalism of cyclic plasticity.” J. Appl. Mech, Trans. ASME, 98(4), 645-651

Dafalias, Y. F. (1987). ” Issues on the constitutive formulation at large elastoplastic deformations, part 1: Kinematics.” Acta Mechanica, 69, 119

Dafalias, Y. F. (1988) ” Issues on the constitutive formulation at large elastoplastic deformations, part 1: Kinetics,” Acta Mechanica, 73, 121

Danielson, K.T. and Adley, M.D. (2000).” A meshless treatment of three-dimensional penetrator targets for parallel computation.” Comput. Mech., 25, 267-273

Dou, H.S. and Phan, T.N. (1998).” On the scalability of parallel computations on a network of workstations.” Comput. Mech., 22, 344-354.

ECCS-Technical Committee 3(1983). European Recommendations for the Fire Safety of Steel Structures. Elsevier Scientific, New York
Giest, A., Beguelin, A. and Dongarra J. (1994). PVM- parallel virtual machine a user’s guide and tutorial for networked parallel computing, The MIT Press

Gropp, W., Lusk, A. and Skjelllum, A. (1994). Using MPI-portable parallel programming with message-passing interface, The MIT Press
Heish, S.H. and Abel, J.F. (1997).” Parallel computation of nonlinear seismic response of steel frames with flexible floors using networked workstations.” J. Chin. Inst. of Civil and Hydraulic Engrg. ,9(1), 77-85

Hsiao, K. M., Horng, H.J. and Chen, Y. R. (1987) “A co-rotational procedure that handles large rotations of spatial beam structures.” Comput. Struct., 27(6), 769-781.

Hsiao, K. M., Lin, J. Y. and Lin, W. Y. (1999). “A consistent co-rotational finite element formulation for geometrically nonlinear dynamic analysis of 3-D beams,” Compt. Meth. Appl. Mech. Eng., 169, 1-18.

Hughes, T. J. R., and Liu, W.K. (1978).
“Implicit-explicit finite elements in transient analysis: Stability Theory,” J. Appl. Mech., ASME, 45, 371-374.

Hughes, T. J. R., Pister, K. S., and Taylor, R. L. (1979). “Implicit-explicit finite elements in nonlinear transient analysis,” Comput. Methods Appl. Mech, Engrg.17(18), 159-182.

ISO 834 (1999). Fire-resistance tests- elements of building construction-Part1: general requirement, International Organization for Standardization, Switzerland

Iwan, W.D. (1967). “On a class of models for the yielding behavior of continuous and composite systems.”J. Appl. Mech., Trans. ASME, 34(E3), 612-617

Izzuddin, B.A., Song, L., Elnashani, A.S. and Dowling P.J. (2000). “An integrated adaptive environment for fire and explosion analysis of steel frames- part II: verification and application.” J. of Construct. Steel Res., 53(1), 87-111

Kirby, B.R. and Preston, R.R. (1987)” High temperature properties of hot-rolled structural steels for use in fire engineering design studies.” Fire Safety J., 13, 27-37

Krieg, R.D. (1975). “A practical two surface plasticity theory.”J. Appl. Mech., Trans. ASME, 42, 641-646

Law, K. (1986).” A parallel finite element solution.” Comput. Struct., 23, 845-858

Li, G..Q. and Jiang, S.C. (1999). “Predicti
on to nonlinear behavior of steel frames subject to fire.” Fire Safety J., 32, 347-368

Lie, T. T. (1992). Structural fire protection, ASCE Manuals and Reports on Engineering Practice No.78

Mamaghani, I.H.P., Shen C., Mizuno, E. and Usami, T. (1995). “Cyclic behavior of structural steels. I: experiments,” J. Engrg. Mech., ASCE, 121(4), 1158-1164.

Mamaghani, I. H. P., Usami, T., and Mizuno, E. (1996). “Inelastic large deflection analysis of structural steel members under cyclic loading,” Engng. Struct., 18(9), 659-668.

Mroz, Z. (1967). “On the description of anisotropic work hardening.” J. Mech. Phys. Solids, 15, 163-175

Ohno, N. (1990). “Recent topics in constitutive modeling of cyclic plasticity and viscoplasticity.” Appl. Mech. Rev.., 43(11), 283-295

Petersson, H. and Popov, E.P. (1977). “Constitutive relations for generalized loadings,” Proc. of ASCE, J. Engrg. Mech. Div., 103(EM4), 661-626.

Poh, K.W. and Bennetts, I.D. (1995). “Analysis of structural members under elevated temperature condition.” J. Struc. Engrg. , ASCE, 121(4), 664-675.

Proe, D. J., I. D. Bennetts, I. R. Thomas and W. T. Szeto (1989). Handbook of fire protection materials for structure steel, Australian Institute of Steel Construction, October

Red Hat Linux 5.2 (1998) The Official Red Hat Linux Installation Guide, Red Hat Software, Inc.

Rice, D. L. and Ting, E. C. (1993). “Large displacement transient analysis of flexible structures.” Int. J. Numer. Meth. Eng, 36, 1541-1562.

Ryan, J.V. and Robertson, A.F. (1959). ”Proposed criteria for defining load failure of beams, floor, and roof construction during fire tests.” J. Res. Nat.l Bureau of Standard, 63C (2), 121-124

Saha, N. and Ting, E. C. (1983). Large displacement dynamic analysis of space frames, EC-SRT-83-5, School of Civil Engineering, Purdue University, IN. U. S. A

Shen, C., Tanaka, Y., Mizuno, E. and Usami T. (1992). “A two surface model for steels with yield plateau,” Structural Eng. /Earthquake Eng., JSCE, 8(4), 179s-188s.

Shih C. (1999). Computational analysis of dry soil containing stiff objects, Ph. D. Disseration, Purde University, W. Lafayette, Indiana

Shivakumar, K.N., Bigelow, C.A. and Newman, Jr J. C. (1992).” Parallel computation in a three-dimensional elastic-plastic finite element analysis.” Comput. Struct. 43(2), 237-245

Storassli, O.O. and Bergen, P.G. (1987).” Nonlinear substructuring for concurrent processing computers.” AIAA J., 23, 871-876

Storassli, O.O., Nguyen, D.T. and Agarwal, T.K. (1990).” The parallel solution of large scale structural analysis problem on supercomputers.” AIAA J., 28,1211-1216

Song, L., Izzuddin, B.A., Elnashani, A.S. and Dowling P.J. (2000). “An integrated adaptive environment for fire and explosion analysis of steel frames- part I: analytical models,” J. Construct Steel Res., 53(1), 63-85

Tang, S. C., Yeung, K. S. and Chon, C. T. (1980). “On the tangent stiffness matrix in a convected coordinate system.” Comput. Struct., 12, 849-856.

Tseng, N.T. and Lee, G. C. (1983).”Simple plasticity model of two surface type.”J. Engrg. Mech., ASCE, 109(3), 795-810.

Usami, T., Gao, S. and Ge, H. (2000).”Elastoplastic analysis of steel members and frames subjected to cyclic loading,” Engrg. Struct., 22(2), 135-145.

Valanis, K.C. (1971).”A theory of viscoplasticity without a yield surface,” Arch. Mech., 23, 517-534.

Valanis, K. C. (1980). “Fundamental consequences of a new intrinsic time measure: plasticity as a limit of the endochronic Theory,” Arch. Mech., 32, 171-191.

Wang, B., Lu, G., and Yu. T. X. (1995). “A numerical analysis of the large deflection of an elastoplastic cantilever.” Struct. Engng. Mech., 3(2), 163-172.

Wang, Y.C. and Moore D.B. (1995). “Steel frames in fire: analysis,” Engrg. Struct., 17(6), 462-472

Wang, Y. K.(1996). A general curved element for very flexible frames, Ph. D. Disseration, Purde University, W. Lafayette, Indiana

Wang, Y. K., Shih, C., and Ting, E. C. (2003). Fundamentals of a vector form intrinsic finite element, CE-ST-2002-001, Department of Civil Engineering, National Central University, Taiwan, R. O. C.

Watanabe, O. and Atluri, S.N. (1986). “Internal time, general internal variable, and multi-yield-surface theories of plasticity and creep: a unification of concepts,” Int. J. Plasticity, 2, 37-57.

Wong, M.B. and Patterson, N. (1996).” Unit load factor method for limiting temperature analysis of steel frames with elastic buckling failure mode.” Fire Safety J., 27(2), 113-122

Yang, T. Y. and Saigal, S. (1984). “A simple element for static and dynamic response of beams with material and geometric nonlinearities” Int. J. Num. Meth. Eng., 20, 851-867.

Yu, T. X., Stronge, W. J., and Liu, J. H. (1989). “Large deflections of an elastoplastic strain-hardening cantilever.” J. Appl. Mech., Trans.ASME, 56, 737-743.