Adaptive Analysis Of Forced Vibrations For Skeletal Systems Based On EEP Super-convergent Method

The adaptive finite element(FE)analysis based on the EEP(Element Energy Projection,EEP)method has been implemented and applied in the static problems.It has also been successfully applied in the analysis of linear forced vibration of one-dimensional rods.A large number of numerical examples verify the effectiveness of the adaptive finite element method in calculating the forced vibration of rods,but there are still some problems to be studied.Based on the adaptive analysis of the linear forced vibration of rods with the EEP method,the stability of Galerkin finite element method(FEM)in the time domain and the validity of the adaptive analysis of the rods under complex loads are thoroughly studied in this paper.Furtherly the whole set of algorithom are extended to the analysis of plane skeletal systems and viscoelastic beams.The main research content of this paper are as follows:1.A preliminary study on the stability of Galerkin FEM in time domain is performed.The original one-step computational solution on the full-time domain is transformed into the equivalent recursive format of time-step solution.The spectral radius method is used to derive the interval of stability of the Galerkin FEM in time domain,and an unconditionally stable format by means of reducing the number of Gauss integration points is also studied in this paper.The convergence of the FE solution and the EEP solution under this format is verified by a typical numerical example.2.The adaptive analysis based on EEP method is performed for the vibration of rods under the complex loads.The sudden load,triangle impulse load and seismic load are applied to engineering problems with practical significance.The comparison between the calculation results and the dense mesh solution of commercial FE software SAP2000 shows that this method is feasible and reliable.3.A self-adaptive finite element analysis method for the linear forced vibration of skeletal systems without considering axial and lateral coupling is studied.For the model problem,the finite element algorithm,the EEP super-convergence solution formulae and the corresponding self-adaptive strategy are given.Fortran90 program is compiled to solve the representative problems.Therefore,this algorithm has achieved initial success in the skeletal systems.4.The adaptive analysis of transversely forced vibration of viscoelastic Euler beams is studied.The transverse forced vibration of viscoelastic Euler beams is the simplest model in road engineering.Based on the Galerkin FEM,the EEP super-convergent formulae for the spatial dimension of the problem are deduced.The algorithm for self-adaptive solving is established and the program is compiled.The results of typical numerical examples show the reliability of the algorithm again.Therefore,the algorithm has achieved another initial success in the viscoelastic problems.