Linear elastic model modeling solving method based on geometric spline

Abstract

The invention discloses a geometric spline-based linear projectile model modeling solving method, which comprises the following steps of: expressing a boundary of a linear projectile problem as a geometric spline of a linear combination of a control vertex and a primary function with geometric significance by using parameters, and finishing modeling; taking a geometric spline primary function withthe same boundary representation model as a shape function of displacement and surface force in a boundary integral equation of the linear projectile problem, obtaining a linear equation set throughthe discrete boundary integral equation, building a stiffness matrix and solving to obtain the displacement and the surface force of a boundary control vertex; according to the method, the physical domain boundary of the 2D line projectile problem is modeled through the geometric spline, an accurate conversion method represented by a common model is provided, and the approximation error of the common boundary model in the modeling stage is avoided; a geometric spline basis function is adopted in a boundary integral equation to serve as a shape function for describing boundary physical quantity, and the model conversion time is saved.

Description

technical field [0001] The present invention relates to the technical field of computer-aided design and engineering, in particular to a linear elastic model modeling and solving method based on geometric splines. Background technique [0002] The existing boundary element method often uses basis functions such as Lagrangian polynomials in the geometric modeling stage, and cannot accurately model a variety of analytical models commonly used in CAD / CAM (computer-aided manufacturing). When using arc splines and trigonometric hyperbolic function curves and surfaces, it is easy to cause model representation errors in the modeling stage. On the other hand, in the existing methods, the basis function of the model representation in the geometric modeling stage is inconsistent with the shape function used in the simulation stage, resulting in repeated model conversions in the modeling and analysis process, which brings large errors and consumes more time. . Contents of the invent...

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Problems solved by technology

[0002] The existing boundary element method often uses basis functions such as Lagrangian polynomials in the geometric modeling stage, and cannot accurately model a variety of analytical models commonly used in CAD / CAM (computer-aided manufacturing), such as the establishment of conic curve surfaces, circular For arc splines and trigonometric hyperbolic function curves and surfaces, it is easy to cause model representation errors in the modeling stage

On the other hand, in the existing methods, the basis function of the model representation in the geometric modeling stage is inconsistent with the shape function used in the simulation stage, resulting in repeated model conversions in the modeling and analysis process, resulting in large errors and more time-consuming

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