[3] Nonlinear Dynamic Analysis Method of Structures

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The Force Analogy Force is a new method for nonlinear analysis of structural seismic hazard. The main idea is to define the local plastic deformation degree of freedom in the structural members and to establish the corresponding local plasticity mechanism to describe the relationship between the internal force and the local plastic deformation,obtain the relationship between overall structure displacement and local shaping mechanism. The method keeps the structural stiffness matrix unchanged during the analysis ,Compared with the traditional variable stiffness method, the stability of the analysis can be guaranteed while the computational efficiency is improved significantly when the dynamic nonlinear analysis is carried out. Force Analogy Method has been extended to the component level and material level.

At the component level: the force-deformation relation of the component is decomposed with elastic-plastic, and the plastic part is expressed by the local plastic hinge, and the control equation based on the force analogy method is obtained. At present, a new model of force analogy method for three kinds of basic structural members is put forward: the bucking model of reinforced concrete columns, the model of shear wall and the modal of axial deformation.

                                                   Figure 1 Model at the component level

At the material level:The basic idea of the force analogy method is extended to the nonlinear constitutive relation, the elastic-plastic decomposition of the strain is carried out, and further combined with the finite element theory, and the element plastic mechanism is established by interpolation, the refined finite element model based on force analogy method is obtained. At present, three basic types of element based on force analogy method are created: fiber beam element, planar element and solid element.

                                     

Figure 2 Model at the material level

                                                          

Publication   

[1] LI G，WONG K. Theory of nonlinear structural analysis: The force analogy method for earthquake engineering [M].John Wiley & Sons, 2014.

Thesis

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[3] GANG L，QIFENG L，HONGNAN L. Inelastic Structural Control Based on MBC and FAM [J].Mathematical Problems in Engineering, 2011, 2011: 

[4] LI G，FAHNESTOCK L A，LI H-N. Simulation of steel brace hysteretic response using the force analogy method [J].Journal of Structural Engineering, 2012, 139 (4): 526-536.

[5] LI G，LI H N. Seismic response analysis of structure with energy dissipation devices using force analogy method [J].The Structural Design of Tall and Special Buildings, 2011, 20 (3): 291-313.

[6] LI G，ZHANG F，ZHANG Y，et al. Nonlinear hysteretic behavior simulation of reinforced concrete shear walls using the force analogy method [J].The Structural Design of Tall and Special Buildings, 2014.

[7] LI G，ZHANG Y，LI H. Nonlinear Seismic Analysis of Reinforced Concrete Bridges Using the Force Analogy Method [J].Journal of Bridge Engineering, 2014, 20 (10): 4014111.

[8] LI G，ZHANG Y，LI H-N. Seismic Damage Analysis of Reinforced Concrete Frame Using the Force Analogy Method [J].Journal of Engineering Mechanics, 2013, 139 (12): 1780-1789.

[9] LI G，ZHANG Y，LI H N. Nonlinear seismic analysis of reinforced concrete frames using the force analogy method [J].Earthquake Engineering & Structural Dynamics, 2014:

[10] SONG S Q，LI G. Inelastic Dynamic Analysis of Steel Structure Using Force Analogy Method [J]. Applied Mechanics & Materials, 2012, 166-169: 304-309.

[11] ZHANG Y，LI H，LI G. Seismic Performance Assessment of Offshore Reinforced Concrete Bridges Using the Force Analogy Method [J]. International Journal of Structural Stability & Dynamics, 2015:

[12] 李钢，余丁浩，李宏男. 基于拟力法的纤维梁有限元非线性分析方法[J]. 建筑结构学报, 2016,  (09): 61-68.

[13] 张宇，李钢，李宏男. 基于拟力法的结构非线性动力分析方法[J]. 地震工程与工程振动, 2014,  (S1): 313-316.

[14] 李钢，李宏男，李瀛. 基于拟力法的消能减震结构地震反应分析[J].土木工程学报, 2009, 42 (4): 55-63.

[15] 李钢，刘啟凤，李宏男. 基于拟力法的MBC非线性控制[J].振动工程学报, 2010,  (03): 324-332.

[16] 宋士强. 基于拟力法的钢结构非线性抗震分析[D]. 大连理工大学, 2012.

[17] 张锋. 基于拟力法的剪力墙结构非线性抗震分析[D]. 大连理工大学, 2015.

[18] 张宇. 基于全寿命周期的近海钢筋混凝土桥梁结构抗震性能分析[D]. 大连理工大学, 2015.