Study On Nonlinear Mechanics Behavior Of Elastic Structure With Different Tension And Compression Moduli

Objective matter world is nonlinear in essence and linear world is only an approximate result from nonlinear one. Materials show the same elastic property in tension and compression, just as classical elasticity theory thought, is also a simplified result from materials nonlinearity. Many tests and researches indicate that materials will display different tensile and compressive strain in absolute value under tensile and compressive stress of the same absolute value, i.e. materials have the nonlinearity with different tension and compression moduli. In fact, most of engineering materials all display different elastic property in tension and compression to some extent. With the development of science and technology, higher requirements are put up to material researches in mechanical performance. To develop new type materials and to explore potential of material properties became the research trend.Elasticity theory with different moduli, founded by Soviet Union scholar Ambartsumyan S.A. in eighties of last century, breaks through the traditional theory on single elastic modulus, puts forward that Young's modulus not only depend upon material property, but also depend upon stress state of point in question, i.e. elasticity modulus is related to material, shape, boundary conditions and external loads of structure and so it is a nonlinear problem resulted from many factors. Elasticity theory with different moduli is a phenomenalism. The researches indicate this theory is consistent with the classical theory. The classical one and its basic equations should be included in the general different moduli theory. Many scholars from home and abroad studied elasticity theory with different moduli, the basic concept and assumptions, analytical solutions for some simple problems and numerical computation of finite element method are proposed successively. Up to now, more study are still needed to solve the existent problems such as the lack of general analytical solution widely used in many fields and convergence, workload and solution accuracy of finite element method. This dissertation tries to use effective analytical methods supplemented with numerical technology to investigate nonlinear mechanics behavior of elastic structure in the range of different moduli theory. The following problems were studied.①Different moduli problems were transformed into classical ones of the same modulus by applying equivalent section method. Under the assumptions of small deformation and plane section, stress and displacement formulas of beam and column under the complex stress state were easily derived. A new quantity, flexural stiffness of different moduli, was introduced. Therefore, the influences brought by different moduli can be entirely considered in flexural stiffness to simplify computation.②Large deflection problem of cantilever beam with different moduli, a unusual problem which have nonlinearity both in materials and in configurations, was solved by pseudolinear analysis and perturbation theory. Perturbation solutions of single parameter can satisfy the common design demands while biparametric perturbation solutions can achieve the sufficient accuracy.③Without the assumption of plane section, approximate elasticity solutions of simply supported beam under uniformly distributed load and of bending-compression column with deadweight and a horizontal force on column capital, were attained. Compared with the solutions from the classical theory, the differences brought by different moduli and the errors introduced by plane section assumption were analyzed.④Based on elasticity theory with different moduli, a new pattern of shear modulus was derived. This formulation is scientific while the former one is empirical and it also effectively solve iterative convergence problem in finite element method.⑤Finite element program of plane problem with different moduli was worked out to run numerical computation of elastic structure. Common bending component, deep bending component and deep beam defined in applicable concrete codes were analyzed in the case of different tension-compression moduli ratios. It is concluded that the different analytical formulas under some assumptions are consistent with the same numerical solutions, that there are different applicable ranges to these analytical formulas and that the former conclusion, position of neutral layer is not related with shear stress, conditionally hold.