6 Nonlinear Finite Element Analysis of Shape Memory Alloy Composite Laminates Ye Ningyi Zheng Zheng Department of Aerospace Design and Applied Mechanics, Beihang University Abstract Hard memory alloy embedded in composite laminates Heart and shape of a text structure. The large deformation of the yttrium-based yttrium alloy brings nonlinearity, and the sinusoidal composite material with several linear analysis functions has an important application prospect in the field of aerospace and other fields. The composite material laminate embedded in the sensor drive element is a shape-remembering shape memory alloy of the smart structure, and the condition is 1.1, the intelligent composite material, and the first-kind drive element. 5 Society as a drive element features can be achieved in a variety of deformation forms, large deformation, easy to be coupled with the substrate, the elastic modulus varies with the state of phase change, limited recovery can produce a great recovery force, therefore, will 98. Combining with composites, through the unique mechanical and physical behavior of 3 people, 8 the shape theory recalls that the structure of the gold complex material satisfies the design requirements for the use.
However, the complex heat engine characteristics of 8 itself make it difficult to use the constitutive relationship of the shape memory alloy Chi 3 composite structure. Considering the non-linear coupling relationship between the stress and strain temperature and the variation of the elastic modulus at different temperatures and the existence of geometrical linearity due to the realization of large deformation, this paper presents a composite material with linear elasticity and geometric nonlinear analysis. Shell element preliminary analysis of the drawing of the shape memory alloy composite lamina into the hall, the results of the calculation of the calculation results of the engineering beam of the needle structure.
1 The shell element equation of the composite shell is a full-stack Lagrangian formula for the finite element equation of the object. Assume that the object is searched from time zero to hour ten, so that the configuration of the time object is the reference frame. At this time, the virtual work principle is force 1 and the strain 1 is the incremental stress of the incremental decomposition degree, incremental strain , Material properties tensor and addition where the formula is substituted into formula 1 and formula 5 and it is noted that the virtual work equation can be reached. The project funded by the National Natural Science Foundation of China, No. 59675036 had different simplifications for the virtual work equation 9. It is generally believed that the items in the 7th integral number are the same order as the first two integral numbers. , the total displacement of the coordinates of the derivative of the coordinate, the former may be greater than the latter. Therefore, the analysis and calculations in this paper are simplified.
Displace any point within the element with a node. After introducing different displacement interpolation functions for different units, formula 67 can be written as a matrix-type displacement strain matrix. Standard points, linear terms, and nonlinear terms.
Using the above two equations, each item in Equation 9 can be written as a matrix in the form of the following, which is an external load.
The equation of the object's balance in the form of a matrix can be obtained where the stress is for each element of yesterday, and 1.1 is the load with the corresponding stress vector.
The concrete composite housing unit and the elements of the matrix in the matrix are available in the literature. This is no longer detailed in row 2 Computational analysis and comparison According to the program compiled by the above basic theory of finite element, the 3-hop 3-wire reinforced composite specimens were calculated and analyzed. The analyzed specimens are the model 1 of the calculation of the beam in the first document. All parameters are taken from the literature 1. The substrate of the test piece is glass-welded, the atomic ratio is 50.8 states, 1 wire; it has a plastic deformation of 3 after pre-stretching, s = 101.1 provides a draw 8 reinforcement, and The simulating line of the constitutive relationship requires 8, the material constants.
Among them, the elastic modulus and thermal expansion coefficient of the substrate, the volume percentage of 3 elbows and 3 filaments. The other 1 is the 9 austenite and martensite state of the elastic modulus, is the phase change coefficient of the thermoelastic coefficient, respectively, the transformation of the stress and temperature when the transformation of the martensite and austenite system â–² â–² The phase transition temperature in the free state.
When performing finite element calculations, an 8-node isoparametric shell element is used.
Elastic modulus, phase transition temperature, 5 , and other shapes 1 have been recalled to the laminate. The linear finite analysis of strain 3 concludes with consideration of the 8 è„Ž 8 driving effect and the composite material, board, and clever results. Compared with the ten calculations in the literature, this algorithm is more accurate and can be used as the foundation for the design and shape control of composite asymmetric laminates.
i Wang Zheng, Wu Jiansheng, Dong Jianwei. Wait. Shape memory alloy wire reinforced composite material Xie Yuquan, He Fubao. Finite element method tilt in elasticity and plasticity. Beijing.
Machinery Industry Press, 1981.
5 He Junyi, Lin Xiangdu. Numerical Solution of Nonlinear Structure of Engineering Structures . Beijing National Defense Industry Press, 19 to accompany.
6 Jiang Qiu, Lu Fengsheng, Gu Zhijian. Composite mechanics river. Xi'an Xi'an Jiaotong University Press, 1990.
Considering the hot load condition, the elastic modulus of the shape memory alloy is a function of temperature.
In the case of small deformation, it is considered that along the direction of the 8 肘 3 wire axis, the strain of the base body and the 3 人 3 wire is coordinated. According to the material mechanics analysis method, the material constitutive relation is derived and the differential form is derived. 13 The dimensional constitutive relationship of silk reinforcement composites.
In practical applications, in. Larger or less rigid bases may have a greater change in recovery of your heartstring. Therefore, there is a large deformation. Under this circumstance, the finite element algorithm in this paper reflects the superiority 1 more suitable for general engineering applications.
65, Finite element calculation results of wire reinforced composite specimens and the results of Wen Hao's calculation.