A Nonlinear GBT-based Beam Finite Element Model And Its Application To Fire And Blast Analyses Of Steel Structures

This dissertation aims at expounding the generalized beam theory?GBT?,and based on that a kind of thin-walled beam element,whose advantage lies on reflecting the local deformations of beams?i.e.,distortion buckling,local buckling,warping shear and plate transverse extension?,was proposed.Then a finite element code built upon the new beam elements,which involves both the material and geometrical nonlinearities,was developed through Fortran programming.It is capable of running the elastopalstic static analysis of prismatic thin-walled members and simulating the fire and blast behavior of restrained steel beams/columns.A thorough validation of the newly developed finite element code was achieved through a series of illustrative examples?e.g.,examples available in the literature?.Results show that the present GBT-based beam finite elements?GBT-BFEs?have great potential to be an alternative to shell finite elements,but exhibit much higher computational efficiency.The present GBT-BFE code is built upon theoretical premises below:?i?the beam element cross-section displacement field is constructed through linear combination of GBT modes,and each of the mode amplitudes only varies along the element length;?ii?the bending related displacements,based on the Kirchhoff's hypothesis,are assumed to be linearly distributed through the plate thickness;?iii?the material in GBT-BFE is assumed to be under plane stress,i.e.,only stress components parallel to the local plate are retained;?iv?to involve the geometrical nonlinearity,the Green-Lagrange strain tensor,which contains higher-order terms,is used to measure reference point deformations,and the PK2 stress tensor work-conjugate to Green-Lagrange strain tensor is adopted as the definition of stress state;?v?the J₂-plasticity with associated flow rule and isotropic hardening is adopted to describe the plastic behavior of structural steels;?vi?a weak-form of the nonlinear equilibrium equations is derived by the Principle of Virtual Work.The numerical discretization and implementation of present GBT-BFE code are based on following schemes:?i?the non-uniform cubic B-splines are used to approximate the mode amplitude functions;the cubic Hermite polynomials are used to approximate the plate mid-plane local deflections;the linear interpolation is used to approximate cross-section out-of-plane warping and transverse membrane extensions;?ii?a implicit iterative method is used to perform the stress updating on each quadrature point,and the consistent tangent modulus,whose calculation can be easily incorporated into the implicit iterative method,is used to calculate element tangent stiffness;?iii?a selective reduced integration scheme is utilized to alleviate locking phenomenon of the present beam element;specifically,only in the calculations of shear deformation related terms and transverse membrane extension related terms the reduced integration scheme is used,but all the other related terms are calculated with full integration scheme;moreover,the Simpson's integration rule is used through the plate thickness;?iv?in the calculation of discrete equilibrium?kinetic?equations,the implicit iterative method is used for fire analyses,and the explicit dynamic method is used for blast analyses.The developed GBT-BFE code consists of three modules,i.e.,?i?pre-processing?i.e.,cross-section discretization,longitudinal discretization,parameter initialization and the most critical GBT cross-section analysis?,?ii?solving and?iii?post-processing?e.g.,result visualizations?.The modules?i?and?ii?concerning the fundamental theories of GBT-BFE was written with Fortran 90 language.To realize the modules?iii?,the data visualization function-ListPointPlot3D in the commercial mathematical software-Wolfram Mathematica is invoked in present code.The present GBT-BFE code was validated against the ANSYS shell-finite elements?SFE?and fire tests available in independent literatures.For fire and blast simulations of steel members,the traditional beam elements can not reflect local deformations?e.g.,local buckling?,so they may lead to unsafe results.A parametric analysis was made to study the influence of local deformations on global fire behavior of restrained steel beams.A series of restrained beams with different boundary restraints subjected to an identical fire scenario were studied by the present GBT-BFE analysis and also traditional beam finite element analysis?TBFEA?,where the TBFE is degraded from GBT-BFE.The final results show that the critical temperatures predicted by the GBT-BFE analysis are much lower than those predicted by the TBFEA.It is reasonable to conclude that local deformations govern the global fire behavior of investigated beams.And no doubt the GBT-BFE is superior to the TBFE for fire simulations of steel members.This research also investigates the thermo-viscoplastic behavior of Q235steel.Through the high temperature split Hopkinson pressure bar?SHPB?tests,the author studied the dynamic responses of Q235 steel at a wide range of temperatures.The test results show that the dynamic strain aging?DSA?influences the temperature-and strain rate-sensitivities of the steel.In the range of DSA,it is visible that the flow stresses of Q235 steel exhibit abnormal thermal strengthening and strain rate softening effects.A new constitutive equation concerning the DSA,which is a multivariable function in terms of plastic strain,temperature and plastic strain rate,is then proposed to describe Q235 steel's thermo-viscoplastic behavior.Because Q345 steel possesses similar dynamic material properties as Q235 steel,its corresponding parameters in the proposed constitutive equation are fitted as well.Finally the new constitutive model was incorporated into the developed GBT-BFE code,so that the blast behavior of steel members can be simulated.