43 results about "Galerkin method" patented technology

The invention relates to an MVP formula-based edge element magnetostatic high-precision calculation method for smooth edges, 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; the polyhedral smooth domain is formed by surrounding corresponding edges by nodes, body centers and face centers of tetrahedron units in the grid data; calculating the vector shape function gradient of the corresponding edge based on the vector shape function of each tetrahedron unit in the polyhedral smooth domain corresponding to the edge; constructing a static magnetic field equation based on an MVP formula and coulomb specifications, and rewriting the static magnetic field equation according to the vector shape function gradient of each edge and a Galerkin method to obtain a system equation of a static magnetic field; further rewriting the system equation of the static magnetic field into a Newton iteration linear equation; and iteratively solving the Newton iteration linear equation by adopting a Newton iteration method until convergence to obtain the magnetic vector position in the static magnetic field. According to the method, the requirements of high calculation precision and stability of the engineering static magnetic field problem are met.

The invention provides an SPH semi-implicit solving method for a landslide and debris flow movement process, and the method comprises the steps: generating a background grid and an SPH particle model of a landslide body or a debris flow body according to the information of a research region and an object source, and applying calculation parameters and boundary conditions; the method comprises the following steps: dividing a momentum conservation equation of a landslide body or a debris flow body into a pressure item, a gradient item and a source item, and carrying out explicit solution on the gradient item and the source item by adopting Runge-Kutta time integral to obtain an explicit speed increment; constructing a finite element solution format for the implicit velocity increment equation by adopting a Galerkin method, and solving to obtain an implicit velocity increment; and combining the explicit speed increment and the implicit speed increment to obtain the SPH particle speed value of the next time step.

The invention discloses a lithium ion battery distributed thermal process sensor fault estimation method. The method comprises the following steps: describing a rectangular lithium ion battery distributed thermodynamic equation by using a two-dimensional partial differential equation; constructing a distributed thermal model of the large-size lithium ion battery; using a Chebyshev-Galerkin method to decompose the distributed thermodynamic equation and the distributed thermal model into reduced-order models described by a standard state space equation in a time domain; a state variable in the reduced-order model is obtained by using sensor measurement output and a Hurvetz matrix construction, and an enhanced reduced-order model is constructed; constructing an enhanced adaptive observer and an error state space equation by using the enhanced reduced-order model; and based on the error state space equation, estimating the fault intensity of the faulted temperature sensor by using a fast adaptive algorithm. The method can effectively estimate sensor faults, including time-invariant and time-varying faults, and single-sensor and multi-sensor faults.

The invention, which relates to the field of intelligent manufacturing, discloses a cooling control system comprising a time-varying analysis module, a monitoring module and an abnormality adjustment module. The time-varying analysis module considers heat conduction and water cooling to construct a regional temperature time-varying model of the pipe die sleeve, adopts a finite element method and a Galerkin method to discretely generate an element matrix equation, and constructs a regional temperature time-varying equation set through the time discretization element matrix equation; the monitoring module obtains the temperatures of all the vertexes and judges abnormity; the abnormity adjusting module carries out multiple rounds of pre-regulation and control when abnormity occurs, simulates the effect of regulating and controlling the opening degree of a valve in each round based on an area temperature time-varying equation set so as to decide to implement regulation and control or continue the next round of pre-regulation and control, and starts optimized pre-regulation and control if the multiple rounds of pre-regulation and control are invalid. And simulating the effect of jointly regulating and controlling the cooling power, the water pumping power and the valve opening degree in each round by the mouse group optimization algorithm based on the regional temperature time-varying equation set to obtain an optimal solution and implement the optimal solution, thereby realizing centrifugal casting cooling control considering regional temperature interaction and control cost.

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 invention relates to the field of electromagnetic calculation, in particular to a frequency domain electromagnetic calculation method of a conformal grid. According to the technical scheme, the method comprises the steps that a calculation area is divided into an inner area and an outer area according to different material attributes and structure attributes of the calculation area, the inner area and the outer area are subdivided by adopting the same grid, and a conformal network is obtained; establishing a functional of the final equation of the outer region, and substituting the outer region and the boundary discrete result thereof into the functional of the final equation of the outer region to obtain a functional of a subunit; accumulating the functional of the sub-regions to obtain a total functional of the outer region, obtaining a differential surface admittance operator through a Gamarin method, and substituting the differential surface admittance operator into the total functional; the total functional is differentiated into zero, a matrix equation is obtained, and outer area field distribution is obtained by solving the matrix equation; and continuously obtaining field distribution of the boundary of the inner region through the longitudinal electric field, and obtaining field distribution of the inner region through an electric field integral equation. The method is suitable for frequency domain electromagnetic efficient calculation of a complex integrated circuit structure.

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 present invention belongs to the technical field of numerical simulation of press riveting connection, and relates to a numerical simulation method of press riveting connection based on a smooth particle Galerkin method, comprising the following steps: S1, establishing a material model; the press riveting nut is regarded as a rigid body, and the thin plate material is regarded as a flexible body; S2, establishing two finite element models of press-in-push-out and press-in-twist-out; only a 1 / 4 model is established for the press-in-push-out, and a full model is established for the press-in-twist-out; S3, performing unit algorithm control; S4, selecting a constraint method to calculate the LS_DYNA contact degree; S5, applying boundary conditions to the press-in-push-out model and the press-in-twist-out model; S6, performing simulation tests, and comparing the experimental results.

The invention discloses a method for regulating and controlling damage of a protective material under a force-heat-oxygen coupling condition, and belongs to the technical field of aerospace, and the method comprises the following steps: S1, constructing a force-heat-oxygen coupling constitutive model of the protective material in a high-temperature, stress and oxidation environment; s2, defining diffusion coefficients of oxygen molecules in the matrix material and the fiber material, taking the diffusion coefficients as functions of damage factors, introducing parameters related to the oxidation degree, and establishing a corresponding constitutive model based on the parameters; s3, developing a finite element calculation program based on a Galerkin method and a Newton-Rafson iteration format; and S4, designing protective materials with different crack characteristics, carrying out modeling simulation by utilizing a force-heat-oxygen coupling model, and analyzing the influence of the crack characteristics on the failure behavior of the protective materials. According to the method for regulating and controlling the damage of the protective material under the force-heat-oxygen coupling condition, the force-heat-oxygen coupling effect is combined, and the damage behavior of the protective material under the action of oxidation and mechanical stress can be accurately described.

The embodiment of the invention discloses a rolling plastic deformation process calculation method and device based on a meshless Galerkin method. The method comprises the steps that a model of a rolling plastic deformation area is established; carrying out approximation on the velocity field function of the node by adopting a moving least square method to obtain a shape function; constructing a system discrete equation based on the shape function and the stream function field; based on the system discrete equation, building a total stiffness matrix by using Gaussian integral point information, a speed boundary condition and a friction boundary condition in a solution domain; building a load force matrix by utilizing boundary point information of the friction boundary; obtaining the speed distribution of each node by using the total stiffness matrix and the load force matrix; obtaining a stable velocity field by adopting a direct iteration method based on the velocity distribution; and calculating the rolling plastic deformation process by using the obtained velocity field. According to the method, the efficiency of calculating the rolling plastic deformation process based on the meshless Galerkin method can be improved.

The invention discloses a method and a system for researching influence of a fixing clamp on fluid-solid coupling dynamic characteristics of a fluid conveying pipeline, belongs to the technical field of coupling dynamics, and solves the problem that the change rule of the displacement of the fixing clamp along with time and space is difficult to accurately express when the fixing clamp transversely moves along with the pipeline. The method comprises the following steps: S1, establishing a transverse motion equation of a flow conveying straight pipe containing a fixing clamp; s2, according to the transverse motion equation, a Galerkin method is adopted for finite term superposition, and the vibration characteristic of the flow conveying straight pipe is obtained; and S3, according to the vibration characteristics of the fluid conveying straight pipe, combining any given working condition to realize fluid-solid coupling dynamic characteristic detection of the fluid conveying pipeline. The method is suitable for various engineering practices needing to consider the fluid-structure interaction vibration problem, such as long-distance gas transmission pipelines, oil exploration systems, urban water supply systems and the like.

The invention discloses a cylindrical lithium battery internal temperature field real-time estimation method and system, and the method comprises the steps: building a temperature space distribution model based on a heat conduction equation, normalizing the space-time quantity through scaling transformation, and converting a non-homogeneous boundary condition into a homogeneous boundary condition through variable replacement; decoupling a space-time relationship between the temperature distribution quantity and a heat production item by adopting a double decomposition technology, and regarding a heat production time variable as a virtual source; and establishing a finite-dimensional ordinary differential equation model by using a Galerkin method. Designing a self-adaptive observer, and estimating a low-order state variable and a virtual source time sequence on line by combining a self-adaptive learning algorithm so as to measure and estimate a temperature error driving update rate; and reconstructing a temperature distribution quantity and a virtual source estimation value through space-time synthesis of the estimation sequence and a preset space basis function. Real-time estimation of the internal temperature field and the heat production amount of the cylindrical lithium battery can be effectively realized by means of a small number of thermocouples only through temperature measurement data without voltage and current sensors.

The invention relates to a high-frequency magnetic element electromagnetic transient characteristic calculation method considering a magnetic core skin effect. An expression of magnetic field intensity in a magnetic core is obtained through an integration method; a hysteresis model is utilized, a Galerkin method is introduced, a magnetic core eddy current field differential equation is obtained, and then a magnetic core boundary magnetic field intensity expression considering hysteresis and macroscopic eddy current is obtained; deducing to obtain a magnetic core lamination boundary magnetic field intensity analytical model considering the magnetic domain mesoscopic eddy current; according to the relationship between the magnetomotive force and the magnetic field intensity and the relationship between the magnetic flux and the magnetic flux density, a total magnetomotive force expression considering the magnetic core skin effect, the hysteresis constitutive relationship and the mesoscopic vortex field is obtained; obtaining a control equation of the electromagnetic transient calculation model of the high-frequency magnetic element by using a magnetic conductance-capacitance analogy method; mesoscopic vortex field parameters and hysteresis model parameters are extracted, and then an electromagnetic transient characteristic calculation model is obtained. According to the invention, the hysteresis characteristic of the magnetic core under complex PWM excitation can be accurately and rapidly simulated, and the accurate and rapid simulation of the actual performance of the high-frequency magnetic element is realized.

The invention discloses a multi-physical field simulation method based on time domain discontinuous Galerkin and finite element mixing, and mainly solves the problems of low calculation speed and high memory consumption of electromagnetic-thermal-mechanical multi-physical simulation. Comprising the following steps: 1) setting the total time step number of simulation and initializing; 2) performing electromagnetic simulation by using a time domain discontinuous Galerkin method to obtain electromagnetic field distribution; 3) performing thermal simulation by using a finite element method based on an electromagnetic simulation result to obtain temperature distribution; 4) correcting the relationship between stress and strain according to the temperature variation of thermal simulation, and performing force simulation by using a finite element method to obtain displacement to obtain a deformation grid; and 5) electromagnetic simulation of the next time step is carried out based on the deformation grid until the total time step number is completely completed, and the multi-physics field simulation task is ended. According to the invention, the speed of multi-physics field simulation can be effectively improved, and the memory consumption is reduced, so that the capability of multi-physics field simulation is improved.

The application discloses a kind of multi-agent collaborative control method and system based on the integration of general sense algorithm wisdom, obtain dynamics, channel, radar, task queue and energy state, construct by Euclidean space, symmetric positive definite matrix manifold and non-negative real number space Generalized state representation;Predict channel state, target trajectory and uncertainty covariance using conditional variational inference network;The prediction result and Lyapunov drift penalty term are introduced into local mean field stochastic state equation and transient stage penalty, and candidate resource strategy and resource marginal technical utility are generated by deep Galerkin method;Under the constraint of total resource, obtain communication, sensing and computing resource allocation vector, according to which adjust event trigger threshold, update parameters and model predictive control solving parameters;Control input is generated under the constraint of control barrier function, and safety fallback quadratic programming is executed when high uncertainty, safety check or solving fails, to realize closed-loop cooperation of resource scheduling, environment prediction and safety control.

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.

The application relates to the field of water conservancy and hydropower engineering, and particularly discloses a soil-rock dam foundation three-dimensional space variability simulation method based on an intermittent Galerkin method, which comprises the following steps: establishing a geometric model of a soil-rock dam foundation; determining probability distribution information of a three-dimensional random field of soil parameters; dividing the three-dimensional random field domain of the soil parameters into three-dimensional random field subdomains; creating base functions in the three-dimensional random field subdomains and assembling a generalized stiffness matrix; calculating eigenvalues and eigenfunctions of an autocorrelation function; extracting standard normal distribution samples and simulating the three-dimensional random field of the soil parameters. The three-dimensional random field domain is divided into a plurality of subdomains, and independent base functions are constructed in each subdomain, so that the independence between the base functions in the subdomains is ensured. The numerical instability of high-order polynomials is eliminated, the assembly format of the generalized stiffness matrix is simplified, and the three-dimensional random field with large scale and high resolution can be generated.

The present invention discloses a dynamic response analysis method for a piezoelectric hybrid functionally graded sandwich hyperbolic plate. Taking into account the deformation compensation control effect of the piezoelectric material in the FGM layer, the relevant dynamic equilibrium equations are established based on the constitutive equations of the piezoelectric material regarding the force, electricity, and thermal coupling of stress, strain, electric displacement, and electric field, as well as the relationship between the electric field and potential. The Galerkin method and Newmark-β method are then used to linearize and discretize the motion differential control equations of the piezoelectric hybrid FGM sandwich hyperbolic plate with a wrinkling effect under the action of a moving load. In the numerical results, the relationships between the temperature rise pattern and action range of the nonlinear temperature field, the action form and movement speed of the moving load, the wrinkle morphology and deformation range, the material performance parameters, the structural geometric parameters, the applied voltage, and the active control on the nonlinear dynamic response of the FGM sandwich hyperbolic plate are discussed.

The application relates to a high-precision calculation method of an edge-smoothed edge element static magnetic field based on an MVP formula, which divides grid data into a plurality of polyhedral smoothing domains with corresponding edges as centers according to each edge in the grid data, and the polyhedral smoothing domain is formed by nodes, body centers and face centers of tetrahedral units in the grid data around the corresponding edge; the vector function gradient of the corresponding edge is calculated based on the vector function of each tetrahedral unit in the polyhedral smoothing domain corresponding to the edge; the static magnetic field equation is constructed based on the MVP formula and the Coulomb norm, and the static magnetic field equation is rewritten according to the vector function gradient of each edge and the Galerkin method, so that the system equation of the static magnetic field is obtained; the system equation of the static magnetic field is further rewritten into Newton iteration linear equations; the Newton iteration method is used to iteratively solve the Newton iteration linear equations until convergence, so that the magnetic vector potential in the static magnetic field is obtained. The method realizes the high calculation precision and stability requirement of an engineering static magnetic field problem.

The present invention discloses a cooling control system, which relates to the field of intelligent manufacturing and includes a time-varying analysis module, a monitoring module and an abnormality adjustment module; the time-varying analysis module considers heat conduction and water cooling to construct a regional temperature time-varying model of a tube mold sleeve, adopts the finite element method and the Galerkin method to discretely generate unit matrix equations, and constructs a regional temperature time-varying equation group through the time-discrete unit matrix equations; the monitoring module obtains all vertex temperatures and identifies abnormalities; the abnormality adjustment module performs multiple rounds of pre-control in the event of an abnormality, simulates the effect of each round of regulating valve opening based on the regional temperature time-varying equation group to decide whether to implement control or continue the next round of pre-control, and starts optimization pre-control if multiple rounds of pre-control are ineffective, simulates the effect of each round of joint control of cooling power, pumping power and valve opening by a rat swarm optimization algorithm based on the regional temperature time-varying equation group to obtain the optimal solution and implement it, thereby realizing centrifugal casting cooling control that considers regional temperature interaction and control cost.

The invention discloses an energy and environmental rock-soil multiphase flow multi-field coupling finite element automatic modeling method. The method comprises the steps that a universal control equation for describing multiphase substance mass conservation, momentum conservation and energy conservation in energy and environmental engineering is deduced based on porous medium mechanics and unsaturated rock-soil mechanics; constructing a weak general format of an energy and environmental geotechnical engineering multiphase multi-field coupling control equation based on a Galerkin method and a Petroleum-Galerkin method; constructing a stiffness matrix of a control equation after multiphase multi-field coupling discretization of the energy and environmental geotechnical engineering; generating an input file of a finite element program automatic generation system FEPG; according to the method, numerical modeling is carried out on energy and environmental rock and soil problems through a unified method.

A calculation method, device and equipment for fluid-structure interaction vibration of a fluid-conveying pipeline, which relates to the technical field of fluid-structure interaction dynamics characteristics of a fluid-conveying pipeline, and solves the technical problem of "how to provide a method for solving fluid-structure interaction vibration of a fluid-conveying pipeline that is widely applicable". The method includes: obtaining the parameters of the fluid-conveying pipeline, fluid parameters and load parameters; establishing the motion equation of the pipeline micro-element and its boundary conditions based on the parameters of the fluid-conveying pipeline, fluid parameters and load parameters; calculating the modal function of the fluid-conveying pipeline by using the differential transformation method based on the motion equation of the pipeline micro-element and its boundary conditions; performing regularization processing on the modal function of the fluid-conveying pipeline; calculating the natural frequency and steady-state displacement response of the fluid-conveying pipeline by using the Galerkin method based on the regularized modal function of the fluid-conveying pipeline and the motion equation of the pipeline micro-element. This method organically combines the differential transformation method and the Galerkin method, has a wider application range, and can be applied to the analysis of fluid-structure interaction dynamics characteristics of fluid-conveying pipelines.

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.

The invention discloses a thermodynamic coupling transient simulation method and system for a complex electronic device, and relates to the technical field of thermodynamic coupling transient simulation. The method comprises the following steps of: discretizing an interpolation approximation equation on a non-equidistant GLL spectrum interpolation node based on an orthogonal basis function to obtain an interpolation function; then a Galerkin method is used, the thermodynamic equation and the solid mechanical equation are weakened through an interpolation function, and a thermodynamic weakening equation and a solid mechanical weakening equation are obtained respectively; and finally, a Newmark-beta implicit iteration method is used to carry out iterative solution on the thermal-mechanical coupling system equation to be solved based on the solved thermodynamic weakening equation and the solid mechanical weakening equation, and a transient temperature field and a stress field are obtained. According to the method, the implicit Newmark-beta method is adopted to support transient simulation of any time step length, so that the transient thermal coupling behavior of a complex electronic device can be accurately simulated, and the calculation efficiency and stability are remarkably improved.

The invention relates to the technical field of power system optimization, in particular to a power grid cross-time scale voltage stability analysis method and system based on a Galerkin method, and the method comprises the steps: improving a transient voltage stability index, carrying out the approximation of the improved transient voltage stability index, and constructing a transient stability boundary function; determining the number of primary functions; determining a polynomial approximation function through the number of the primary functions; obtaining a simplified system equation under the condition of no discrete switching event; applying a Galerkin method to obtain a continuous polynomial approximate expression; according to a continuous polynomial approximate expression and the trigger condition function, obtaining a system state after a discrete event occurs; taking the jumped system state as a new initial condition, and obtaining a continuous polynomial approximate expression after a discrete event occurs; and then a polynomial approximation result is used for model prediction control, and full-time-scale stable risk quantification is realized. According to the invention, the accuracy of power grid cross-time scale voltage stability analysis is improved.

The invention discloses a method and a system for studying the influence of inner wall roughness on flow-induced vibration characteristics of a flow conveying pipeline, belongs to the technical field of coupling dynamics, and solves the problem that a transverse motion differential equation of the pipeline under the influence of variable roughness is difficult to accurately express. The method comprises the steps that S1, a transverse motion equation of the variable-roughness fluid conveying pipeline is established; s2, according to the transverse motion equation, a Galerkin method is adopted to carry out finite term superposition, and a characteristic solution of the fluid conveying pipeline is obtained; and S3, according to the characteristic solution of the fluid conveying pipeline, combining with any given working condition to realize the flow-induced vibration characteristic detection of the fluid conveying pipeline. The method is suitable for application scenarios such as fluid conveying pipeline system design optimization.

The invention discloses a calculation method suitable for full-sea-depth underwater explosion shock waves and bubble loads, and relates to the field of underwater explosion. The method solves the problems that a double-exponential formula in a shock wave stage of an existing theoretical model for underwater explosion load calculation cannot reflect the attenuation rule of shock wave pulse width and water depth and does not conform to the actual situation. The method comprises the following steps: setting a working condition of underwater explosion, and determining an initial condition required by calculation; the method comprises the following steps: calculating an underwater explosion shock wave load based on an intermittent Galerkin method under a spherical symmetric projection coordinate system, switching underwater explosion load calculation from a shock wave stage to a bubble stage, and switching a shock wave load calculation method to a far-field shock wave propagation model solved by adopting the intermittent Galerkin method; and solving the bubble equation by adopting a Runge-Kutta method to obtain a physical quantity of underwater explosion, calculating a bubble load at a specified measuring point in water based on a potential flow theory, and calculating full-sea deep-water underwater explosion shock wave and the bubble load.