5 results about "Secant method" patented technology

The invention relates to the technical field of tunnel construction grouting filling, in particular to a calculation method and system for a tunneling type tunnel construction grouting filling extrusion diffusion mechanism, and the method comprises the following steps: dispersing a slurry diffusion area at a grouting hole to obtain a plurality of fan-shaped units; performing iterative calculation on the grouting flow and the pressure field of the ith fan-shaped unit based on a secant method; according to the pressure difference of the ith fan-shaped unit, the variable quantity of the construction gap thickness is calculated, and the construction gap thickness is updated; in each calculation step, the diffusion radius and the grouting flow corresponding to each fan-shaped unit are recorded, so that the pressure distribution condition of the grout at each discrete point in the diffusion area is obtained, meanwhile, the thickness of the construction gap is dynamically updated according to a pressure change result, and geometric boundary conditions are provided for next iteration. According to the method, disturbance of slurry filling and diffusion to construction gaps is considered, and the method is closer to actual interface change.

The invention discloses a thin-walled workpiece milling deformation regulation and control optimization method combining an intelligent algorithm and error compensation, and belongs to the technical field of numerical control machining low deformation and machining process optimization. Comprising the following steps: constructing a thin-wall part finite element dynamic milling model and a milling process parameter vector set; solving by using a finite element analysis method to obtain a corresponding machining deformation result as a sample data set; constructing a particle swarm algorithm with the minimum machining deformation as an optimization target and the maximum removal rate as a boundary condition to optimize the technological parameter vectors to obtain an optimal milling technological parameter vector combination; measuring a machining error and using a double-point secant method as a machining error compensation iterative algorithm to obtain a machining error compensation value; and based on the optimal milling process parameter vector and the machining error compensation value, the thin-wall part is milled. According to the method, the technological parameter combination optimization and the error compensation strategy are combined, and the machining quality and the machining efficiency of the thin-wall part in the milling process are improved.

The invention discloses an electric power system saddle node bifurcation point solving method based on a hybrid estimation-correction and secant method, and belongs to the technical field of electric power system stability analysis. The method comprises the following steps: establishing an extended power flow equation set; obtaining an effective initial value through a pre-estimation-correction method; dynamically processing a network equation for a line fault scene; judging a bifurcation point interval based on the linear relation and the sensitivity; and combining a secant method with self-adaptive step length control to realize accurate positioning of the bifurcation point. According to the method, the defect that the numerical value is unstable near the bifurcation point in the traditional method is overcome, the calculation efficiency and robustness are improved, the method is suitable for a complex power system containing faults and new energy, and effective support is provided for stability analysis.

This application discloses a method for solving damage evolution parameters in a damage constitutive model, belonging to structural mechanics and fracture mechanics. The method includes: establishing a mathematical relationship between damage variables and associated variables based on thermodynamic principles, and obtaining an integral expression for the energy dissipation potential per unit volume by combining damage evolution criteria; simplifying the integral expression for the energy dissipation potential per unit volume based on the principle of equivalent strain, obtaining a scalar analytical expression; numerically integrating the scalar analytical expression using the three-point Newton-Cotes integration algorithm, and iteratively solving for the damage evolution parameters using the secant method. This method transforms complex tensor operations into simple scalar analysis, reducing the computational burden. Furthermore, the use of the Newton-Cotes integration method and the secant method iterative solution strategy ensures accurate calculation of damage parameters, enhances computational stability and reliability, and significantly improves the efficiency and accuracy of the solution.

The invention discloses a method for solving damage evolution parameters in a damage constitutive model, and belongs to structural mechanics and fracture mechanics, and the method comprises the steps: building a mathematical relationship between a damage variable and a concomitant variable according to a thermodynamic principle, and obtaining an integral expression of energy dissipation potential per unit volume in combination with a damage evolution criterion; on the basis of the equivalent strain principle, the integral expression of the unit volume energy dissipation potential is simplified, and a scalar analysis expression is obtained; and carrying out numerical integral solution on the scalar analytic expression by utilizing a three-point Newton-Cotes integral algorithm, and iteratively solving damage evolution parameters by adopting a secant method. According to the method, complex tensor operation is converted into simple scalar analysis, the calculation burden is reduced, the Newton-Cotes integral method and the secant method are adopted to iterate the solving strategy, accurate calculation of damage parameters is ensured, the stability and reliability of calculation are enhanced, and the solving efficiency and accuracy are remarkably improved.