Research On Energy Finite Element Analysis And Its Application To Composite Laminate Plate

Energy Finite Element Analysis (EFEA) is a numerical analysis method for high frequencyvibration analysis. It uses the time-averaged and space-averaged energy density as the primaryvariable to form the governing differential equations, which can be numerically calculated by finiteelement method. The averaged energy density of the whole system can be obtained. The results ofenergy density can then be transferred into measurable kinematics parameters, such asdisplacement, velocity and acceleration, etc.At high frequency, conventional finite element analysis (FEA) methods require a largenumber of elements to capture the high frequency characteristic of the structures, which results invery long computational time and high costs. Reasonable results even can’t be obtained foruncertainty factors. Until recently, many papers and reports have been published about isotropicstructures. However, not much work has been done in the field of composite structures.Research on EFEA method for isotropic structures is presented and summarized in thisdissertation. The EFEA governing differential equation is developed for rod, beam and plate. Thepower transmission characteristics at rod-rod and beam-beam junctions are studied to obtain thepower transmission coefficients, which are utilized to compute the joint matrix. The joint matrix isneeded to assemble the global system of EFEA equations, which can be solved numerically and theenergy density distribution within the whole system can then be obtained.To improve the performance of composite materials and utilize their full advantages, it iscrucial to have an effective prediction of their response subjected to impact loads in the practicalengineering problems. Research for developing EFEA formulation for modeling compositelaminate plates is Studied. The multilayer laminate plate is assumed to be equal to one-layeranisotropic plate using classical laminate theory. Then the one-layer anisotropic plate can further besimplified to be isotropic plate using the average concept, such as average damping and averagegroup speed. The global system of EFEA equations can be numerically solved and the energydensity distribution within the entire system can be obtained based on the research work ofisotropic structure. Therefore, the vibration response can be predicted in the early design period.