11 results about "Galerkin method" patented technology

The application belongs to the field of gear transmission system squeeze film damper damping, especially relates to a kind of gear squeeze film damper damping quick calculation method and system, obtains the structural parameter of squeeze film damper, carries out velocity calculation and constructs the Reynolds equation of squeeze film damper oil film pressure;Based on half-step center finite difference method, the Reynolds equation is solved, and the oil film distribution pressure of oil film damper is obtained;Based on oil film distribution pressure, the oil film counterforce of oil film damper is calculated using double integral algorithm.Compared with the classical short bearing approximate solution and long bearing approximate solution, its use range is wide, and compared with super relaxation iteration method, its calculation efficiency is high.Make it can be used in gear dynamics model to carry out damping analysis.When solving fluid Reynolds equation by finite difference method, only the working condition with regular boundary condition can be processed.Based on variational principle and Galerkin method, a new more general finite element method is proposed to calculate the oil film counterforce of SFD.

The application relates to the technical field of composite material analysis, and discloses an online thermal analysis method and system for composite materials and a storage medium, which comprises multi-physical field coupling modeling, a thermal response coupling model containing solid-gas phase interaction is constructed, a correlation relationship between parameters and temperature and decomposition reaction progress is established, spatial discretization is carried out by using the Galerkin method, a thermal response differential equation set is solved by using an implicit or explicit time stepping algorithm, temperature field distribution, mass loss and carbon layer formation data are obtained, the carbon layer formation standard is that the mass fraction of a matrix is reduced by 20%, the carbon layer thickness is calculated by mass loss, a mechanical property parameter model is established, and the residual strength after a fire is calculated, and a temperature-time curve, residual strength distribution and parameter sensitivity analysis report can be visually displayed on an online platform. The application realizes full-process analysis from thermal response simulation to residual strength evaluation, improves prediction accuracy, and reduces the application threshold.

The invention discloses a grounding grid electrical impedance imaging method based on an adaptive smooth Newton method. The method comprises the following steps: S1, constructing a mathematical model of grounding grid electrical impedance imaging; s2, solving a correction problem: S21, dispersing a grounding grid field domain into triangular unit grids; s22, converting the Laplacian equation into a weak form by adopting a Galerkin method; s23, potential distribution is solved; s3, solving the inverse problem; S31, constructing a target function; s32, constructing a smooth functional, and performing continuous differentiable smooth approximation on a total variation regularization item in the target function; s33, dynamically adjusting the smoothing parameter by adopting a homotopy continuation strategy, and performing iterative solution based on the smoothed target function to obtain reconstructed conductivity distribution; and S4, generating an electrical impedance image of the grounding grid. The grounding grid electrical impedance imaging method effectively improves the accuracy and stability of grounding grid electrical impedance imaging, and is suitable for solving inverse problems such as grounding grid electrical impedance imaging.

A high-performance simulation method for heat conduction and thermal stress of embankment in non-homogeneous half-space. Based on the principle of geometric similarity transformation, the method constructs a scaling boundary modeling strategy, introduces a scaling line coordinate system, realizes the spatial mapping of Cartesian coordinates to scaling coordinates, and uses the Jacobian matrix to complete the coordinate transformation of differential operators, thereby accurately representing the non-uniform characteristics of the medium material. The Galerkin method is used to establish the control equation, and the semi-analytical solution technique is used to obtain the temperature field distribution; then the fourth-order Runge-Kutta algorithm is used for reverse iteration to further calculate the thermal stress field caused by the temperature field. The invention can effectively solve the problems of high calculation cost, complex boundary modeling and poor interface continuity of existing numerical methods in non-homogeneous media. It has high computational efficiency, excellent numerical stability and high precision characteristics, and is suitable for thermal-mechanical coupling analysis of complex engineering structures such as multi-layer foundation, embankment-water-foundation coupling system, etc.

The application discloses a three-dimensional integrated microsystem electric-thermal cooperative calculation method based on a meshless Galerkin method, and comprises the following steps: establishing a background integral grid based on a three-dimensional integrated microsystem model, and establishing integral points by using grid and boundary information; finding integral points in a solution domain, and determining field nodes of a support domain where the integral points are located; calculating a shape function and a derivative thereof at each integral point; obtaining a temperature stiffness matrix and a node thermal load matrix at a boundary, and a basic temperature stiffness matrix and a basic node thermal load matrix based on the shape function and the derivative thereof; adding electric-thermal coupling terms in the basic temperature stiffness matrix and the basic node thermal load matrix to obtain a temperature stiffness matrix and a node thermal load matrix in a discrete domain; and obtaining a temperature field of the three-dimensional integrated microsystem model according to the temperature stiffness matrix and the node thermal load matrix at the boundary, and the temperature stiffness matrix and the node thermal load matrix in the discrete domain. The application eliminates the influence of grid shape on a solution result, and ensures precision.

The invention provides an enhanced meshless Galerkin numerical method for calculating a steady-state wave propagation problem, and belongs to the field of numerical simulation calculation and numerical forecasting of the steady-state wave propagation problem, and the method comprises the steps: dispersing a steady-state wave propagation problem computational domain into a node set, constructing a physical field variable initial interpolation format based on a meshless Galerkin method, and carrying out the numerical simulation calculation of the steady-state wave propagation problem. Deriving a node interpolation function; selecting a combination of a first-order Lagrange polynomial and a trigonometric function as a local strengthening primary function, and introducing a new node degree of freedom to construct a local strengthening interpolation; the unit decomposition characteristics are maintained, a global interpolation format is constructed, a numerical model is established in combination with a partial differential equation and a Galerkin method, and a physical field variable of any point is solved after conditions are applied. According to the enhanced meshless Galerkin numerical value method for calculating the steady-state wave propagation problem, the problem of insufficient precision of a traditional meshless Galerkin numerical value method in wave propagation problem numerical calculation is solved.

The invention provides a method and a system for calculating electromagnetic scattering characteristics of a complex target and a medium. The method comprises the following steps: dividing regions according to material distribution and splitting open regions into open regions and interfaces; constructing an electromagnetic current joint integral equation based on electric field and magnetic field continuity conditions; the equation is directly adopted in an open area, and a variable coefficient is introduced into an interface to correct a Robin transmission condition; constructing a matrix equation by using a full / semi-RWG primary function and combining a Galerkin method through a triangular surface element discrete grid; and after a generalized minimum margin method is adopted for solving, a scattering field and a radar scattering sectional area are calculated. According to the method, variable coefficient DDM, non-conformal mesh generation and discontinuous Galerkin technologies are fused, the problem of discontinuity of multi-scale adaptation and matrix construction is solved, calculation precision and efficiency are both considered, and the method is suitable for rapid calculation of electromagnetic scattering of complex targets.

This invention relates to the field of geotechnical engineering, specifically to a method, medium, and equipment for simulating random fields in rock masses within fault zones of railway tunnels. The method includes: meshing the rock mass space within the fault zone of the railway tunnel; interpolating through nodes within the mesh; artificially reducing the dimensionality of the three-dimensional random field covariance structure of the rock mass; introducing the Galerkin method to perform K-L expansion to solve for eigenvectors and eigenvalues; solving for the number of truncated terms in the K-L expansion; and generating random field samples based on the eigenvectors, eigenvalues, and the number of truncated terms in the K-L expansion. This invention, by establishing a rock mass mesh in the fault zone of a railway tunnel that satisfies finite element mechanical simulation, combined with the Galerkin method's weak form integral equation solution method for finite element analysis, achieves efficient and accurate simulation of parametric random fields under spatial variations of rock mass parameters in fault zones of railway tunnels. Furthermore, this method can be used to handle complex rock mass geometric conditions, demonstrating strong practical engineering significance.

The application discloses a cylindrical lithium battery internal temperature field real-time estimation method and system, first, a temperature space distribution model is established based on a heat conduction equation, normalized space-time volume is obtained through scaling transformation, and a non-homogeneous boundary condition is converted into a homogeneous one through variable replacement; a double decomposition technique is used to decouple the space-time relationship between the temperature distribution volume and the heat production volume, and the heat production time variable is regarded as a virtual source; a finite-dimensional ordinary differential equation model is established by using a Galerkin method. An adaptive observer is designed, a low-order state variable and a virtual source time sequence are estimated online in combination with an adaptive learning algorithm, a temperature error is measured and estimated, and an update rate is driven; through space-time synthesis of an estimated sequence and a preset space base function, a temperature distribution volume and a virtual source estimated value are reconstructed. Only temperature measurement data are required, voltage and current sensors are not required, and real-time estimation of the cylindrical lithium battery internal temperature field and the heat production can be effectively realized with the aid of a small amount of thermocouples.

The invention relates to a transient electromagnetic field-circuit coupling high-precision calculation method based on an A-alpha formula, and the method comprises the steps: dividing grid data into a plurality of polyhedral smooth regions with corresponding edges as centers according to the edges in the grid data of a three-dimensional motor 1 / 8 periodic model; a smooth vector shape function of edges and a smooth shape function of nodes in the polyhedron smooth domain are calculated; constructing a transient field-circuit coupling equation set based on an A-alpha formula, transient eddy current and coulomb specifications, and rewriting the transient field-circuit coupling equation set according to the smooth vector shape function of each edge, the smooth shape function of each node and a Galerkin method to obtain a transient field-circuit coupling system equation; further rewriting the transient field-circuit coupled system equation into a Newton iteration linear equation; and iteratively solving the Newton iteration linear equation by adopting a Newton iteration method until the Newton iteration linear equation converges to obtain a magnetic vector bit in field-circuit coupling, thereby realizing high-precision numerical solution of the transient field-circuit coupling problem in the complex motor system.

The application discloses a kind of three-dimensional tip clearance dynamic response simulation analysis method and system of crack-containing blade, comprising: for blade radial vibration, crack is equivalent to blade radial tensile spring, the natural frequency of blade radial vibration and mode equation are calculated;For blade bending vibration, crack is equivalent to torsional spring and blade width / thickness direction tensile spring, the natural frequency of blade bending vibration and the mode equation of displacement and cross-section rotation angle caused by bending are calculated;With equal-section torsional blade with through crack at trailing edge as research object, according to Hamilton principle, combined with Galerkin method, the dynamic model of crack-containing blade is established, the dynamic model is solved and the dynamic response of crack-containing blade tip surface is obtained;According to the geometric relationship between the dynamic response of blade tip surface and the deformation of blade, the three-dimensional tip clearance dynamic response of crack-containing blade is calculated.The method thus provides guidance for aero-engine blade crack fault diagnosis based on three-dimensional tip clearance.