finite element equation
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2020 ◽  
Vol 34 (14n16) ◽  
pp. 2040077
Author(s):  
Zhongyun Xiao ◽  
Bin Mou ◽  
Xiong Jiang ◽  
Wei Han

A framework of numerical formulations for the aeroelastic analysis of helicopter rotor is presented in this paper. The blade structural dynamics are modeled by an open source multibody dynamic software MBDYN, which solves finite element equation of elastic bodies in general motions. Then the structural deformation is transformed to blade surface grid by radial base function (RBF) interpolation, and volume grids are regenerated by RBF and TFI methods. Lastly, the fluid governing equations are solved. By integrating the above methods, S76 hovering rotors are simulated and compared to the test data. Results show that elastic torsion decreases local angle of attack. For status at [Formula: see text] and [Formula: see text], the shock and shock-induced separation are reduced on the outboard blade, which has remarkable effects on the prediction of rotor hovering performance.


Author(s):  
Bo Zhou ◽  
Zetian Kang ◽  
Zhiyong Wang ◽  
Shifeng Xue

Abstract It is significant to numerically investigate thermo-mechanical behaviors of shape memory alloy (SMA) structures undergoing large and uneven deformation for they are used in many engineering fields to meet special requirements. To solve the problems of convergence in the numerical simulation on thermo-mechanical behaviors of SMA structures by universal finite element software. This work suppose a finite element method to simulate the super-elasticity and shape memory effect in the SMA structure undergoing large and uneven deformation. Two scalars, named by phase-transition modulus and equivalent stiffness, are defined to make it easy to establish and implement the finite element method for a SMA structure. An incremental constitutive equation is developed to formulate the relationship of stress, strain and temperature in a SMA material based on phase-transition modulus and equivalent stiffness. A phase-transition modulus equation is derived to describe the relationship of phase-transition modulus, stress and temperature in a SMA material during the processes of martensitic phase transition and martensitic inverse phase transition. A finite element equation is established to express the incremental relationship of nodal displacement, external force and temperature change in a finite element discrete structure of SMA. The incremental constitutive equation, phase-transition modulus equation and finite element equation compose the supposed finite element method which simulate the thermo-mechanical behaviors of a SMA structure. Two SMA structures, which undergo large and uneven deformation, are numerically simulated by the supposed finite element method. Results of numerical simulation show that the supposed finite element method can effectively simulate the super-elasticity and shape memory effect of a SMA structure undergoing large and uneven deformation, and is suitable to act as an effective computational tool for the wide applications based on the SMA materials.


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