38 results about "Finite element equation" patented technology

The invention belongs to the technical field of oil and gas production and development, and discloses a sand production pressure difference and sand production quantity quantitative prediction method suitable for a high-temperature and high-pressure sandstone reservoir, which comprises the following steps: calculating static rock mechanical parameters of a target well; predicting initial crustal stress; establishing a porosity and permeability dynamic evolution model; establishing a three-dimensional finite element model; establishing a seepage stress coupling transient nonlinear finite element equation; applying well bottom pressure drop to simulate production, and determining sand production pressure difference; and establishing a sand production rate prediction model, and quantitatively predicting the sand production rate. According to the method, factors such as pore permeability stress, temperature change and water content influencing rock strength are comprehensively considered, a three-dimensional finite element model is established, a seepage stress coupling finite element equation and solving steps are established based on a reservoir elastic-plastic consolidation theory, critical plastic strain is introduced to quantitatively characterize the sand production risk, a sand production prediction model is established, and the rock strength is predicted. And finally, quantitative and accurate calculation and scientific pressure control of the critical sand production pressure difference and the sand production amount are realized.

The invention relates to the technical field of geophysical exploration, and particularly provides a three-dimensional finite element transient electromagnetic forward modeling calculation method based on an iterative solution method.The method comprises the steps that tetrahedron space discretization is carried out based on a vector finite element method, and an electric field is given to six edges of a space tetrahedron; constructing a back-pushing Euler finite element equation set, and assembling a linear system formed by a large sparse matrix based on the equation set; performing iterative solution on the linear system based on an FGMRES algorithm to obtain an electric field value corresponding to a spatial tetrahedron unit edge; optimizing a spatial tetrahedral mesh based on a quadratic nesting method, and optimizing a time step length based on a third-order backward Euler difference format; a grid pre-encryption method is adopted, the calculation error of iterative solution is reduced, a region decomposition method is used for achieving parallel calculation, and the calculation efficiency is greatly improved. According to the method, the requirements of high precision and high efficiency in three-dimensional transient electromagnetic forward modeling calculation can be met, and an advanced calculation tool is provided for resource exploration in a complex geological environment.

The invention provides a parallel iteration solving method and system for an electromagnetic finite element equation set, and relates to the technical field of electromagnetic finite elements, and the method comprises the steps: constructing a to-be-solved electromagnetic finite element equation set # imgabs0 #; dividing the electromagnetic finite element equation set into a plurality of calculation sub-tasks, and distributing a sub-matrix block # imgabs 1 # and a sub-right-end item vector # imgabs 2 # of the sub-tasks to each process in the super computer; by means of the initialized Hoseholder-GMRES algorithm, the processes are subjected to subtask calculation in parallel, and the local optimal solution # imgabs3 # of each process is obtained; summarizing the local optimal solution # imgabs4 # of each process to obtain an optimal solution # imgabs5 # of the electromagnetic finite element equation set; according to the method, the electromagnetic finite element, the Householder-GMRES algorithm and parallel computing are combined, and the solving efficiency of the linear equation set of the electromagnetic finite element is improved by utilizing a parallel optimization technology.

The invention relates to the technical field of computer-aided engineering, in particular to a nonlinear efficient iterative solving method for thermal strain load, which is used for solving an obtained finite element equation by using a modified Newton-Raphson method and comprises the following steps of: firstly, establishing a geometric model to be analyzed and performing grid division; the method comprises the following steps: firstly, setting a model to be analyzed, then setting boundary conditions and temperature field change conditions of the model to be analyzed, finally, inputting the conditions into an algorithm solver, solving a nonlinear equation set, iteratively inputting a load continuously according to a modified Newton-Raphson method in the solving process, calculating node displacement until convergence, and solving stress-strain conditions in the welding process according to a material constitutive relation. In the solving process, by judging the size of the two norms of the displacement increment obtained in the adjacent increment step heuristic stage, the convergence of nonlinear solving of the structure is enhanced through the calculation mode, and the solving speed of the nonlinear problem in the thermal elastic-plastic constitutive structure is increased.

The invention relates to the technical field of transient heat conduction, in particular to a composite material transient heat conduction and thermal stress simulation method based on a two-dimensional arbitrary polygon hybrid finite element, which comprises the following steps: S1, determining an analysis model and material attributes, and establishing a transient heat conduction basic equation including boundary and initial conditions; s2, constructing and expanding a generalized variational functional, processing boundary conditions in combination with a Lagrange multiplier method, and discretizing a solution domain into a plurality of independent units; s3, adopting hypothetical temperature field, heat flux field and thermal stress field functions, introducing a discrete finite element format, and deducing a corresponding finite element equation from a functional; and S4, solving a transient temperature field through programming, introducing the transient temperature field into stress analysis, and finally obtaining temperature and stress distribution of the material at different time points. According to the method, temperature distribution and thermal stress of transient heat conduction are solved by hybridizing heat flux finite elements, and a new way is provided for transient heat conduction and thermal stress analysis of the composite material.

The invention discloses a stiffness matrix compression storage method and system based on block symmetry characteristics and a medium, and the method comprises the following steps: constructing a geometric model, and obtaining material attribute parameters; dividing finite element analysis grids according to the geometric model, and numbering units, nodes and degrees of freedom; setting boundary conditions and load applying conditions; a storage space is applied based on the block symmetry characteristic of the global stiffness matrix; calculating an element stiffness matrix, assembling element stiffness matrix information to a global stiffness matrix, and applying a boundary condition; and solving a finite element equation corresponding to the compressed and stored global stiffness matrix by adopting a numerical solution method. According to the method, the reducibility of the stiffness matrix is kept, redundant information stored in the stiffness matrix is reduced, and the time complexity of the stiffness matrix and vector multiplication and other matrix operation is also reduced, so that the solving performance of the linear equation set is effectively improved.

The invention provides a wave finite element and boundary element mixed composite board structure sound insulation performance prediction method, and the method belongs to the acoustics field, and comprises the steps: carrying out the post-processing of a wave finite element model based on the wave finite element model of a composite board structure and a corresponding equivalent nodal force, and obtaining the wave finite element equation of the whole composite board structure; based on a sound-structure coupling equation, through a boundary element method, a discrete boundary element equation related to the surface vibration speed of the composite board and the radiation sound wave pressure is constructed; coupling the wave finite element equation and the discrete boundary element equation of the whole composite board structure, and determining the sound pressure of radiation sound waves of the composite board structure and the surface vibration speed of the composite board; and based on the sound pressure of the radiation sound wave of the composite board structure and the surface vibration speed of the composite board, obtaining a sound insulation performance prediction result by calculating the sound power of the incident sound wave and the radiation sound wave, and completing prediction of the sound insulation performance of the composite board structure. The problems that the sound transmission loss of large plates and medium-high frequency plates is difficult to predict and the calculation cost is high are solved.

The invention relates to a physical field coupling simulation analysis method and device of a circuit breaker, computer equipment, a computer readable storage medium and a computer program product. The method comprises the following steps: acquiring distributed conductivity in an arc extinguish chamber of the circuit breaker; according to the distributed conductivity and an electric field finite element equation, an electric field distribution value in the circuit breaker arc extinguish chamber is obtained through calculation; calculating a current density distribution value in the arc extinguish chamber of the circuit breaker based on the electric field distribution value; substituting the current density distribution value into an axisymmetric magnetic field equation, and performing electric field and magnetic field coupling; substituting the port boundary voltage and the port current of the arcing area of the circuit breaker into the circuit matrix equation, and carrying out electric field and circuit bidirectional coupling; the electric field finite element equation, the axial symmetry magnetic field equation and the circuit matrix equation are combined, and the potential distribution value and the magnetic field distribution value of the arcing area of the circuit breaker and the port boundary voltage and the port current of the equivalent resistor are obtained through solving. By adopting the method, the simulation analysis efficiency and precision of the circuit breaker arc extinguish chamber can be improved.

The invention discloses an electromagnetic simulation method and system based on a variational finite element method. A calculation area is set; defining two auxiliary vector fields on an artificial truncation boundary; performing projection on the two auxiliary vector fields in each far-field direction by using a finite element basis function, and calculating an expansion coefficient in each far-field direction; constructing a finite element equation stiffness matrix and a boundary matrix; and according to the near-field electric field, the stiffness matrix, the boundary matrix and the expansion coefficients of the two auxiliary vector fields in the current far-field direction, calculating an electromagnetic far-field component in each far-field direction. By introducing a variational finite element method, precision loss caused by geometric boundary complexity or medium heterogeneity in a traditional integration method is eliminated. A phase factor is directly embedded into the auxiliary vector field, electromagnetic wave propagation characteristics are accurately represented, calculation reliability is ensured, and electromagnetic simulation requirements of a large-scale simulation domain can be met by improving the conversion process from a near field to a far field.

The invention relates to an in-hole transient electromagnetic response characteristic numerical simulation method based on a tunnel three-dimensional geoelectric model and an absorption boundary finite element method, and belongs to the technical field of geophysical exploration. The method comprises the following steps: constructing a tunnel full-space three-dimensional conductivity model; based on a Maxwell equation set, a vector potential and a scalar potential are introduced, a vector control equation of a transient electromagnetic field is derived in combination with Coulomb specifications, first-order absorption boundary conditions are established, and a weak form finite element equation is derived through a Galerkin weighted margin method; generating a global sparse matrix by utilizing spatial discretization and unstructured grid division, and performing iterative solution on the dynamic electromagnetic field by adopting a Newmark time discretization method; and simulating the transient electromagnetic response of geological anomalous bodies with different resistivity and the distance between the geological anomalous bodies and the receiving coil, and analyzing the attenuation characteristic and the geometric gravity center effect to obtain an electromagnetic response rule. The device can accurately simulate the electromagnetic response of abnormal bodies such as aquifers and faults in front of a tunnel face and around drill holes.

The present application belongs to the technical field of numerical simulation of laser directed energy deposition, and relates to a numerical simulation method for the influence of process parameters on the temperature field of laser directed energy deposition of Inconel 718. When calculating the transient temperature field distribution in the process of laser directed energy deposition, the present application needs to complete the definition of material properties, the establishment of a geometric model and mesh division, the establishment of a transient temperature field control equation, the application of a heat source, the application of initial conditions and boundary conditions, the discrete processing of a transient temperature field finite element equation set, latent heat processing, and iterative solving of several parts of work. The numerical simulation method of the present application studies the temperature distribution law in the process of laser directed energy deposition of Inconel 718 material, analyzes the influence of process parameters on the temperature field, establishes and perfects the theoretical basis of laser directed energy deposition of Inconel 718 material, and guides the formulation of process parameters, which has important scientific research significance and engineering application value.

The invention belongs to the technical field of power equipment insulation structure design, and discloses a transient thermal field rapid calculation method of a direct current wall bushing and a related device. An energy conservation equation is discretized in time and space, and a finite element equation based on a pre-established finite element simulation model is established; simplifying the finite element equation to obtain a rapid calculation equation; during simplification, the earliest moment influencing transient thermal field distribution of the direct current wall bushing at any moment is determined, and influence items of thermal field distribution at the moment before the earliest moment in the finite element equation on the transient thermal field of the direct current wall bushing at any moment are deleted; determining a heating coefficient in the rapid calculation equation at any moment to obtain a rapid calculation model corresponding to the rapid calculation equation; and calculating the transient thermal field distribution of the direct-current wall bushing at any moment according to the rapid calculation model. According to the method, rapid calculation of transient thermal field distribution of the direct-current wall bushing can be met.

This invention belongs to the field of computer vision and non-rigid point cloud registration technology, and specifically to a scale-adaptive non-rigid point cloud registration method based on gradient decoupling. It includes the following steps: S1: Solving for the stiffness matrix and node multimodal eigenvectors; S2: Solving for the optimal matching point index and robust weights; S3: Solving for the scale gradient and deformation gradient; S4: Solving for the updated scaling coefficients. This invention achieves parameterized separation of scale mismatch and local physical deformation by explicitly introducing a continuously differentiable scale factor into the physical finite element equations and combining it with a spatial orthogonal gradient decoupling strategy. This not only solves the problem of numerical convergence instability caused by misjudging "volume expansion" in traditional methods when scale mismatch occurs, but also ensures that the algorithm maintains stable registration accuracy under scale disturbances.

The application relates to a kind of transient load under the function gradient porous structure of multiphase filling dynamics topology optimization method and system, belong to the topology optimization design field of function gradient porous structure.The technical problems to be solved by the application are: how to fully exploit design space, construct the efficient function gradient porous structure of multiphase filling dynamics topology optimization method, realize the optimal anti-vibration design of porous filling structure with high-quality transient dynamic performance.Technical points: based on characteristic orthogonal decomposition method, the reduced transient dynamic finite element equation of function gradient porous multiphase filling structure is constructed;the material interpolation model and volume constraint model of function gradient porous multiphase filling structure are constructed, and the transient dynamic multiphase filling topology optimization reduced model with the minimum dynamic compliance as the optimization objective is proposed;the reduced sensitivity time-domain accompanying equation is constructed, and the sensitivity of dynamic compliance and volume constraint is efficiently calculated;based on ADMM-MMA hybrid optimization algorithm, the optimal topology design of function gradient porous multiphase filling structure is efficiently solved and obtained.The application can maximize the optimal anti-vibration performance of function gradient porous filling structure, and is especially suitable for the structure lightweight anti-vibration design of large engineering equipment.

The present invention discloses a method for calculating the temperature rise of an oil-immersed power transformer, which relates to the technical field of grid digitization and is used to solve the problem of low efficiency in existing temperature rise calculations. The method includes the following steps: obtaining physical property parameters, finite element node mesh data, and boundary conditions, and based on the physical property parameters, finite element node mesh data, and boundary conditions, using the least squares-upwind finite element method, through an initial solution optimization algorithm, combined with the fluid-thermal coupling finite element equation, obtaining an initial solution optimization equation; solving the initial solution optimization equation through a POD-ATS-HTS hybrid variable step size algorithm to obtain the transient temperature rise. The present invention also discloses an oil-immersed power transformer temperature rise calculation device, an electronic device, and a computer storage medium. By combining the initial solution optimization algorithm with the hybrid variable step size algorithm, the present invention improves the calculation efficiency of the temperature rise.

The present application belongs to the field of structural deformation reconstruction, and specifically discloses a structural deformation reconstruction method and system based on a four-node inverse plate shell element containing a drilling degree of freedom, comprising: discretizing the structure into a plurality of four-node inverse plate shell elements, and constructing a shear strain matrix by using a discrete shear gap method; kinematically constraining the drilling degree of freedom by using a continuum mechanics rotation field, solving the continuum medium rotation by deriving the global coordinate system from the natural coordinate system shape function, and supplementing the sixth degree of freedom of the element around the normal line; deriving a coordinate transformation matrix based on the assigned sixth degree of freedom, introducing a node coordinate system, transforming the element stiffness matrix to the node coordinate system, and then transforming it to the global coordinate system; and finally, incorporating the above construction method into the least squares functional framework, assembling the global inverse finite element equation by minimizing the error between the theoretical strain and the measured strain, and reconstructing the full-field displacement of the structure. The present application can realize high-precision deformation reconstruction of complex stiffened plate shells and large-curvature structures.

The invention relates to the field of thin film antennas, in particular to a thin film antenna form analysis method and system considering crease factors. Constructing a finite element model of the folded membrane structure based on the folding scheme; the finite element model comprises a fold unit finite element equation, a cable membrane unit and structure finite element equation and boundary relation processing of fold units; designing an optimization model of the folded membrane structure based on the finite element model, including defining design variables and constraint conditions, constructing a multi-objective optimization problem according to the design variables and the constraint conditions, and converting the objective optimization problem into a single-objective function; and performing iterative solution on the single objective function based on a genetic algorithm to obtain the optimal form of the folded membrane structure. According to the method, the shape and stress design of the folded film structure can be effectively realized, the system modeling and analysis of the film antenna crease problem can be realized, the influence of the crease on the stress uniformity of the film structure can be improved in combination with an optimization algorithm, the stress uniformity of the effective area of the film can be ensured, and wrinkles in the film can be effectively avoided.

The present invention relates to a method for predicting a three-dimensional stress field around a spiral perforating and fracturing well, comprising the following steps: S1, constructing a formation-wellbore-perforation three-dimensional model of a target block according to actual basic parameters; S2, discretizing the formation-wellbore-perforation three-dimensional model and performing grid division; S3, constructing a finite element equation of the three-dimensional model, solving the finite element equation, and predicting the stress field. The method of the present invention can accurately predict the stress field distribution around the spiral perforating well and the wellbore under any phase angle condition, thereby providing a basis for fracturing optimization design.

The application discloses a ground penetrating radar time domain finite element fast simulation method, system and equipment. The method comprises the following steps: setting geometric parameters and electrical parameters of a two-dimensional complex geoelectric model; constructing a weak form of a two-dimensional electromagnetic wave equation; forming a time domain finite element equation; establishing a linear equation group after central difference time discretization; giving a time step, judging whether the time step meets a CFL stability condition, if yes, directly solving the linear equation group, if not, performing LU decomposition on a coefficient matrix of the linear equation group, and disturbing unstable eigenvalues in the coefficient matrix until absolute values of all eigenvalues of the decomposed coefficient matrix are less than or equal to 1, and generating a reconstruction coefficient matrix; and solving the reconstructed linear equation group, so that the time step breaks through the CFL stability condition. The application can improve the simulation precision of the ground penetrating radar.

The invention belongs to the technical field of structural finite element data processing, and particularly relates to an iterative solution method and device for a finite element equation set of a whole machine structure. The method comprises the steps of obtaining a complete machine structure sparse positive definite stiffness matrix and a load vector applied to a complete machine structure, and constructing a complete machine structure finite element equation set used for representing the relation among the complete machine structure sparse positive definite stiffness matrix, the load vector and a displacement vector; performing degree-of-freedom elimination on the sparse positive definite stiffness matrix of the whole machine structure to obtain an independent degree-of-freedom matrix; performing bandwidth optimization sorting on the independent degree-of-freedom matrix to obtain a sorted stiffness matrix; processing the sorted stiffness matrix based on an algebraic multi-grid preprocessor to obtain a preprocessed sub-matrix; and calculating a displacement vector by adopting a conjugate gradient iteration method according to the pre-processing sub-matrix. According to the method, the problem that the sparse matrix of the aviation structure is not converged in iterative solution can be effectively solved, and the solution efficiency is remarkably improved while the calculation precision is ensured.

The invention relates to a porous composite material equivalent thermal expansion coefficient calculation method based on energy homogenization, and belongs to the technical field of calculation materials, and the method comprises the following steps: S1, establishing an energy homogenization theoretical basis for calculating an equivalent thermal expansion coefficient; s2, deducing a finite element equation of the equivalent thermal stress coefficient based on energy homogenization based on the theoretical basis of energy homogenization for calculating the equivalent thermal stress coefficient established in the step S1; and S3, solving the equivalent thermal expansion coefficient of the porous composite material based on the finite element equation of the equivalent thermal stress coefficient based on energy homogenization deduced in the step S2. According to the new method provided by the invention, the obtained equivalent thermal expansion coefficient is under the double-precision condition of 15-bit effective digits, and the same effective digits of the calculation result reach 12-13 digits; and under the grid density of 100 * 100-1000 * 1000, the calculation efficiency is improved by about 60%-70%.

The present invention discloses a method, system, and medium for compressing and storing a stiffness matrix based on block symmetry. The method comprises the following steps: constructing a geometric model and obtaining material property parameters; dividing a finite element analysis grid according to the geometric model and numbering the units, nodes, and degrees of freedom; setting boundary conditions and applying load conditions; applying storage space based on the block symmetry of the global stiffness matrix; calculating the unit stiffness matrix, assembling the unit stiffness matrix information into the global stiffness matrix, and applying boundary conditions; and solving the corresponding finite element equations after compressing and storing the global stiffness matrix using a numerical solution method. The present invention maintains the reducibility of the stiffness matrix, reduces the redundant information stored in the stiffness matrix, and reduces the time complexity of stiffness matrix-vector multiplication and other matrix operations, thereby effectively improving the performance of solving linear equations.

The present invention provides a finite element analysis method for realizing automatic water diversion of a water diversion pipe in a PC-PRB, including: determining the water diversion flow rate of the water diversion pipe based on the length of the water diversion pipe, the permeability coefficient, the water flow cross-sectional area, and the groundwater head at the starting point of the water diversion pipe and the center point of the water distribution layer; constructing a finite element equation group based on solving the seepage problem, and determining the coefficient matrix formula according to the finite element equation group; after the water diversion pipe is introduced into the target PC-PRB model, based on the SOR iterative solution method, the water flow calculation is performed according to the coefficient matrix formula; the water flow calculation includes constructing the finite element equation of the water inlet node of the water diversion pipe under the condition of stable flow and the groundwater head at the starting point of the water diversion pipe and the center point of the water distribution layer under the condition of unsteady flow; based on the water flow calculation, considering the single point injection scenario and the planar injection scenario, the parameters of the coefficient matrix formula are adjusted to realize the finite element analysis of the automatic water diversion of the water diversion pipe in the PC-PRB. The present invention can realize the automatic water diversion function of the pipeline.

The invention relates to a field-circuit coupling simulation method and system of a transformer, computer equipment and a medium. According to the field-circuit coupling simulation method of the transformer, the magnetization curve of the to-be-tested transformer is fitted through a high-order interpolation method, so that the stability and the precision when a nonlinear finite element equation of an electromagnetic field of the transformer is solved are effectively improved, the stability of field-circuit coupling simulation of the transformer is ensured, the numerical oscillation phenomenon generated by field-circuit coupling simulation of the transformer is avoided, and the reliability of field-circuit coupling simulation of the transformer is improved. According to the method, the operation efficiency and reliability of transformer field-circuit coupling simulation can be improved, meanwhile, the calculation amount of nonlinear equation solving is effectively reduced, the solving efficiency is improved, and the efficiency of transformer field-circuit coupling simulation can be improved.

The invention relates to the technical field of electromagnetic field analysis and unmanned aerial vehicle inspection, in particular to a power transmission line unmanned aerial vehicle inspection safety distance electromagnetic field analysis method and system, and the method comprises the steps: building an electromagnetic field model of a power transmission line through a Maxwell equation set, and representing an electromagnetic field as a discretized finite element equation set; performing approximate processing on node potential and magnetic vector potential through energy functional of the electric field and the magnetic field in combination with a shape function, and solving electric field distribution and magnetic field intensity at the node; and in combination with simulation calculation, simulating the equivalent radius and charge distribution characteristics of a power transmission line conductor, and calculating the minimum safe flight distance of the unmanned aerial vehicle in the inspection task. The method has the advantages that accurate modeling and simulation analysis are conducted on the electromagnetic field of the power transmission line through the finite element method, and the safety and efficiency of unmanned aerial vehicle inspection operation are remarkably improved.

The invention relates to the technical field of numerical simulation of metal materials, and discloses a numerical simulation method for creep behavior of metal after pre-oxidation, which comprises the following steps: establishing a finite element model of the creep behavior of the metal after pre-oxidation; a finite element equation of metal high-temperature oxidation simulation is established according to a mechanical-chemical coupling model of high-temperature oxidation simulation, a user-defined unit subprogram is written according to the finite element equation, and the user-defined unit subprogram is used for calculating metal high-temperature oxidation; writing a user material subprogram according to the constitutive model of metal creep, wherein the user material subprogram is used for calculating creep deformation and creep damage; and the creep behavior of the metal after pre-oxidation is simulated in a mode of calling a user material subprogram in a user-defined unit subprogram. Through numerical simulation, related data of the creep behavior of the metal after pre-oxidation can be obtained without a test, and manpower and material resources are saved.

The application discloses a kind of gear dynamic engagement stiffness calculation methods, comprising: obtaining the geometric parameters of gear pair, material attribute and gear motion state parameter;Calculate overall stiffness matrix, overall mass matrix, overall damping matrix and overall external load matrix;Establish the dynamic analysis finite element equation when gear engagement, solve the dynamic vibration displacement of engagement point at different time by using average acceleration method;According to dynamic vibration displacement, the dynamic stiffness of two gears in gear pair is calculated, and single-tooth engagement stiffness is obtained;According to the coincidence degree of gear pair, single-tooth engagement stiffness is superimposed to obtain dynamic engagement stiffness;Also disclosed is a kind of device, including motion state module, three-dimensional scanning module and processing module.The application is based on finite element method, not only considers the influence of angular position change on engagement stiffness, but also considers the influence of gear speed on gear engagement stiffness, more truly reflects the dynamic characteristics of gear when transmission, so that the calculation result is more accurate.

The present invention belongs to the technical field of finite element analysis methods, and in particular relates to a dimensionality reduction analysis method for finite elements. It includes the following steps: extracting the basic variable sequence of the finite element model to establish a basic model; collecting or designing samples to be analyzed to generate a finite element model; establishing a finite element mathematical model based on the structural finite element equilibrium equation; designing and determining the fuzzy interval of the finite element variables; based on the fuzzy variable set segmentation processing, involving fuzzy variable differential processing, based on Taylor series fuzzy variable stiffness optimization, finite element equilibrium equation global stiffness optimization, determination of displacement response, and solving separately in the subset interval. This application expands and simplifies the fuzzy variables involved in the finite element analysis process, and derives the optimization calculation through the actual physical relationship between the basic structural set parameters of the finite element equation, which can better simplify and optimize the calculation and analysis process when fuzzy parameters are involved, improve the operation efficiency, and reduce the time consumption of finite element analysis.

The present invention discloses a flexible manipulator control method and system based on finite element discretization and modal order reduction, including: dividing the flexible manipulator connecting rod into a plurality of units; constructing the motion control equation of any unit of the flexible manipulator after discretization; establishing the finite element motion control equation of each unit, assembling the finite element motion control equation of each unit to obtain the global dynamic finite element equation of the flexible manipulator; solving the generalized eigenvalue problem of the global dynamic finite element equation to obtain the modal vibration shapes of each order of the flexible manipulator; performing order reduction transformation on the global dynamic finite element equation based on the modal vibration shapes of each order to obtain the reduced global dynamic finite element equation; and performing motion control on the flexible single-rod manipulator of the robot based on the global dynamic finite element equation. The present invention can realize the effective suppression and precise control of the vibration of the flexible manipulator.

The present invention discloses an electromagnetic simulation method and system based on the variational finite element method. The present invention sets a calculation region; defines two auxiliary vector fields on the artificial truncation boundary; projects the two auxiliary vector fields in each far-field direction using the finite element basis function #imgabs0# to calculate the expansion coefficients in each far-field direction; constructs the stiffness matrix #imgabs1# of the finite element equation and the boundary matrix; calculates the electromagnetic far-field components in each far-field direction according to the near-field electric field, the stiffness matrix, the boundary matrix, and the expansion coefficients of the two auxiliary vector fields in the current far-field direction. By introducing the variational finite element method, the present invention eliminates the accuracy loss caused by the geometric boundary complexity or medium inhomogeneity in the traditional integral method. The auxiliary vector field directly embeds the phase factor to accurately characterize the electromagnetic wave propagation characteristics, ensuring the calculation reliability. At the same time, by improving the near-field to far-field transformation process, it can meet the electromagnetic simulation requirements of large-scale simulation domains.