Isogeometric Approach For Static And Dynamic Analysis Of Beam Structure

As a new numerical analysis method,isogeometric theory uses the same formulation for geometric models and analytical models,and the geometrical error introduced by complex finite element mesh can be avoided.Meanwhile,direct interaction between design and analysis can be achieved by using isogeometric analysis.As important load-bearing components,the mechanical analysis of beam structures is widely concerned and studied.Therefore,the purpose of this dissertation is to combine isogeometric theory with beam theory to complete the derivation of algorithms for linear elasticity,geometric nonlinearity,and free vibration of isogeometric spatial beam structures,and to validate the algorithms using three types of structures: straight beam,constant curvature beam,and variable curvature beam.The specific research work includes:(1)Based on basic kinematic assumptions,adopting non-uniform rational B-splines(NURBS)basis functions to interpolate the geometric shape of the beam and the displacement of control points,a linear elastic analysis formulation for isogeometric beam structures based on a mixed interpolation element method is derived.Using different interpolation functions for the displacement terms and strain terms of the structure solves the locking problem in the calculation process.The algorithm program is completed.The results of a numerical example analysis show that the mixed interpolation method can effectively avoid locking effects.Additionally,the solving rules of the algorithm are summarized: the higher order and the more refined elements,the more accurate results will be.(2)According to the Total-Lagrange method,using the initial configuration of the model described by spline geometry as the reference configuration,the geometric nonlinear analysis formulation of isogeometric beam structures is derived.The Newton-Raphson method is used for iteration,and the incremental step size is dynamically adjusted to simulate the nonlinear deformation process.The algorithm program is completed.The results of numerical example analysis verify the effectiveness of the geometric nonlinear algorithm.Compared to commercial finite element software,the algorithm calculates fewer degrees of freedom to obtain highprecision solution.(3)Hamilton’s principle is used to obtain the dynamic formulation of isogeometric beam structures.Then the natural frequencies and vibration modes of the model are determined,and the free vibration analysis algorithm is programmed.The final results verify the effectiveness of the free vibration analysis algorithm with high computational efficiency and accuracy.When analyzing straight beam structures,the proposed algorithm exhibits stronger robustness compared to commercial finite element software.The algorithm derived in this dissertation effectively analyzes the static and dynamic mechanical problems of beam structures,and constructs an efficient and feasible solution for the simulation analysis of spatial beam structures.