Numerical Study For Mechanical Characteristic Having Different Young's Moduli In Tension And Compression

It is well known that tensile modulus is assumed the same as compressive modulus in the classical theory of elasticity. However, many engineering materials, especially new materials, that are widely developed and applied, such as powder metallurgical materials, polymeric material, composite materials, etc, have different strength when they are loaded with tension and compression, respectively. Most of them behave distinctive mechanical characteristics, one of which is different Young's moduli. With the development of science and technology, some research turns into a new study trend to develop new materials and to explore potency of material speciality in itself. The theory breaks through the assumption the elastic modulus is only related to the properties of material itself. The elastic modulus is related to the material, shape, boundary condition and external loadings of structures. So it is a nonlinear problem contributed by many factors.The finite element method (FEM) has been applied to many engineering fields. As the mechanical properties of the materials have not been clarified, the finite element method for the different modulus problem is not widely developed and applied in practical engineering. With the development of contemporary engineering materials, the materials with different Young's moduli in tension and compression will be widely used in engineering. Therefore, it is necessary to develop an effective numerical method in order to correctly analyze the mechanical properties of these materials.This thesis focuses on developing a new finite element formulation and iterative algorithm for different Young's moduli in tension and compression. Numerical study of mechanical properties is presented for the structures having different moduli in tension and compression.Ambartsumyan's FE model, Jones' FE model and Ye's FE model are improved and investigated by an equivalent and complete concept. The FEM for different Young's moduli in tension and compression is further perfected with error estimation and dimensionless formulations. Equivalent is proven between the criterion of the principal strain presented by Ye's and the criterion of the principal stress widely used by predecessors. The dimensionless formulations of the principal material matrix and stiffness matrix develop the finite element method for different moduli.The corresponding FEM program is established with Matlab platform. Numerical study is presented for the elastic problems having different moduli. The neutral axis problem and the ratio influence of tensile modulus to compressive modulus are discussed for bending structures under various conditions, such as different geometric models, different loads. With increasing the difference between tensile modulus and compressive modulus, there exits large errors in the value and distribution of displacement and stress, if classical theory is used to solve the problems having different Young's moduli in tension and compression.The different tension-compression elastic moduli are introduced into small-displacement and large-displacement finite element formulations and numerical methods are developed using modified. Three-dimensional finite element iterative program for geometric and material nonlinear analysis is established.Numerical study is presented for load-carrying capacity problem of different modulus structures. The influential factors of load-carrying capacity are further discussed, including constraint conditions, couple moments, ratios of tensile modulus to compressive modulus, etc. Finally, results show that there are big errors of load-carrying capacity in the bending-compression members having different moduli by using uniform modulus model.