Elasto-plastic Time-history Analysis For Short-leg Shear Wall Structure Based On Precise Exponential Matrix Algorithm

The system of short-leg shear wall structure was early used in the southern region of China.The theory study of the system is always fallen behind the engineering application, especially in earthquake-resistant capability.Then it is necessary to establish a new mechanical model and to analyze elastc-plastic seismic response,which can provide the scientific basis for the high-rise buildings with short-leg shear wall in the vast earthquake zone.The contradiction among the accuracy,stability and time consuming of elasto-plastic time-history analysis is becoming increasingly conspicuous,which conditioned the development of the structural dynamic analysis.That requires to propose better implicit methods saving storage spatial and computing time or explicit methods of high accuracy and better stability.Precise time step integration method(PTSIM)has the advantage of high accuracy but it is difficult to calculate the multi-dimensional matrix if apply the PTSIM directly to structural dynamic analysis.Therefore it is a meaningful work to develop new explicit or implicit dynamic time-history methods based on the advantage of precise exponential matrix algorithm of PTSIM and apply them on seismic analysis of short-leg shear wall structure.Based on those,some work has been done as follows:1.Summarize the development and application actuality of precise time step integration method in detail,which provide the basis for the proposed method.2.The PTSIM is much easier to be understood by complete and detailed derivation.Two kinds of integral schemes are proposed.The PTSIM based on numerical integration is analyzed and validated overall,and numerical integration of upper calculation efficiency for PTSIM is selected.By introducing the numerical integral term,application ranges of PTSIM are widen.3.Based on the precise exponential matrix algorithm,Newmark - RPDTSIM(renewal precise direct time step integration method)is put forward by coupling the Newmark method and RPTSIM.The integral scheme is not related to parameterβ.Basic formulas are introduced and deduced and explicit and implicit algorithms are presented to Newmark-RPDTSIM.4.Two kinds of integral schemes are respectively proposed to explicit or implicit algorithm of Newrnark-RPDTSIM.The stability and accuracy of the two integral schemes are analyzed.Results prove that the first scheme is conditional stable and better accurate while the second one is unstable by the developed program of MATLAB.5.Load values of three time points are need to be calculated in Newmark-RPDTSIM.If the load is arbitrary,the values of every time points were difficult to get.Then the explicit and implicit Taylor series algorithms are put forward.The curves between spectralρ,algorithmic damping ratio(?),amplitude decay AD,period elongation PE and sampling frequencyΩare drawn and characteristics of stabilities and accuracies are analyzed by the developed program of MATLAB.6.With the examples of constant load and sine load,characteristics of accuracy and transcendency for explicit and implicit Taylor series integration methods are further analyzed. The total deformation theory and incremental theory of are put forward explicit integral method with Taylor series.7.The PTSIM,RPTSIM and the proposed explicit Taylor series method are applied to elastic and elastic-plastic seismic analysis of short-leg shear wall structure whose results are compared with those of Newmark-βmethod and Wilson-θmethod.The developed program SLWPISA of MATLAB is able to draw displacement curve,speed curve and acceleration curve of the building under earthquake actions.Inter-story displacements and the happening time of inter-story maximum displacement and shear force can be gained.8.The example results show that the explicit integral method with Taylor series is suitable to earthquake action and is reasonable.Because the proposed method is explicit, which means it is not necessary to calculate the coupled equations,it is superior to use the method on large practical structures.The results of the proposed method and Wilson-θmethod are generally approximate,which of the other three methods are partly approximate under the rare earthquake effect.The above analysis shows that the applicability of a specific integral method is rely on many factors of nonlinear types,nonlinear degree and load characteristics. Then a better nonlinear time integration program must consist two or two more integral methods when one method is unsuitable the others can be chosen.9.The results of example show bottom strengthened stories should be set and restrained edge members should be installed in walls intersection when short-leg shear wall structure is designed.High-rise building should not be all shear wall structures of short-leg shear wall in real engineering because the stiffness of short-leg shear wall structure is smaller than that of general shear wall structure and its inter-story displacement is lager.When short-leg shear wall is more in a high-rise building,barrel or general shear wall should be set.Then the shear wall structure is formed to carry horizontal loads by barrel and short-leg shear wall.