Refined Second-order Elastic Analysis of Latticed Shell Structures
|Keywords||latticed shell structures second-order elastic analysis space beam element precise displacement expression multivariate deformation coupling|
Latticed shell structures are extensively used in many projects of long-span structures. Resently, the research regarding the accuracy and applicability of both analytical model and methods of latticed shell structures is far to be sophisticated. In order to implement the second-order elastic analysis of latticed shell structures under external force, it is necessary to develop a precise analytical model and method in a comprehensive, systematical and thorough way. Hereinafter, based on some existing research work in the available literatures, according to the solid mechanics and nonlinear finite element method, a research on precise analytical model and method of shell structures are carried out and the results are presented in this paper.Based on the finite deformation theory, the mechanics of latticed shell structures in nonlinear analysis are discussed. Instead of the traditional multiple displacement interpolation theory, a new displacement interpolation stability function based on beam-column model and element tangent stiffness matrix for nonlinear analysis are derieved in this paper, which can exactly reflect the movement and deformation of the elements. Moreover, not only the independent effect of tension, compression, shear, and torsion, but also the multivariate coupling of these factors are considered in the calculation of nodes’displacement and strain. Displacement interpolation function without axial force effect is derived as well, which could be implemented in the first load step where the components’axial force is zero and stability functions are ineffective.A new beam element analytical model with two nodes and 12 DOF is proposed, which takes bowling effect, axial-deformation and bending coupling, axial-deformation and shear coupling, axial-force and torsion coupling and bidirectional bending and flexural-torsional coupling into account. Based on the incremental theory, element tangent stiffness matrix is derived from virtual work equation, which can reflect the multivariate coupling of different deformation and make the model applicable in geometric nonlinear analysis. By introducing the relationship between force and displacement of nodes, a precise analytical model and second-order analytical method of shell structures are obtained.With load increment method, a computing program based on the precise analytical model and second-order analysis method is complied by MATLAB language. Regarding to the inconvenience and cumbersomeness resulting from two different expressions for displacement interpolation functions which differs according to whether the axial-force is positive or negative, a power series method is introduced in this paper regardless of whether axial force is tensile or compressive, and according to some numerical analysis, a necessary numbers of terms (N) is suggested. Numbers of numerical examples not only verify the accuracy of the proposed precise analytical model and method of shell structures, but also indicate the main factors affecting the calculation accuracy and efficiency, which is the neglect of axial force effect in element stiffness matrix. In general, the analytical model and method are improved and optimized.