Flexible body structure high-order nonlinear finite element numerical simulation method based on quintic Hermite shape function

Abstract

The invention discloses a novel flexible body structure high-order nonlinear finite element numerical simulation method based on a quintic Hermite shape function, and the method comprises the steps: deducing a quintic Hermite interpolation shape function and an attribute equation based on a quintic Hermite high-order interpolation theory; determining a flexible body structure unit and parameters, a physical model and a simplified hypothesis which need to be solved by the flexible body structure unit; establishing a mathematical motion partial differential equation of the flexible body structure unit in space and time and axial stretching limiting conditions, namely solving a mathematical model in a domain; and establishing a system equation of the flexible body structure unit, and adopting a Newton iteration method to carry out iterative solution on the parameters. The beneficial effects are that simulation precision of space deformation, rotation angle and curvature of the slender flexible body structure is improved; the continuity of the curvature at finite element nodes is ensured; rapid convergence is achieved, and particularly the prediction precision of the high-order vibration frequency of the flexible body is higher; and when the problems of transverse large gradient load and large bending of the flexible body are solved, higher precision guarantee is provided.

Description

Technical field [0001] The present invention relates to the field of Slender Structures, which is specifically a high-order nonlinear finite element numerical simulation method based on flexible body structure based on five Ermite. Background technique [0002] As of now, the finite element method of the most commonly used flexible body structural unit (such as a beam unit) is still a finite element method based on the Cubic Hermite Shape Functions. The method can only ensure the continuity of the first order derivative of the spatial configuration and the shape of the form (ie the angle slopeangle) in finite element discrete nodes. [0003] Since the spatial morphology of the flexible body unit structure is simulated in three times a polynomial function, the first order derivative is a secondary function of the space, that is, the secondary distribution, the secondary derivative is a single function, i.e., linear distribution. This method although it is already a good numerical ...

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Problems solved by technology

Although this method has achieved good numerical simulation accuracy, it has some inherent defects: the simulated results of this method can only guarantee the continuity of the first derivative of the space shape of the space flexible structure at the finite element nodes, but cannot guarantee the continuity of the second derivative. The continuity of the order derivative function; and the Dirichlet boundary condition cannot be applied to the boundary condition of the flexible body unit whose curvature is zero, resulting in deviation (deviation) between the physical model and the numerical model boundary condition; when the flexible body is subjected to When there is a large gradient load (that is, when the distribution of bending moment and shear force inside the structure undergoes a large mutation), it is difficult for the algorithm to accurately capture the extreme position and magnitude of the bending moment and shear force (position and magnitude of the critical bending moment and shear force), requires very fine finite element elements to capture these extreme values

It is difficult to accurately predict the natural frequency of the high-order vibration of the flexible body structure by using the cubic Hermitian finite element method, and there will be a large error, and the coarser the element, the greater the error

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