Magneto-structural analysis determines structural deformation resulting from the magnetic forces acting on a current-carrying conductor or magnetic material.
Applications involve determining forces, deformations, and stresses on structures subjected to steady-state or transient magnetic fields from which you want to determine the effects on structural design. Typical applications include pulsed excitation of conductors, structural vibration resulting from transient magnetic fields, armature motion in solenoid actuators, electromagnetic acoustic transducers, and magneto-forming of metals.
The following related topics are available:
To perform a direct magneto-structural analysis, use one of the element types summarized in Table 2.28: Elements Used in Magneto-Structural Analyses. For detailed descriptions of the elements and their characteristics (degrees of freedom, KEYOPT options, inputs, outputs, and so on), see the individual element descriptions.
For more information on the magnetic formulations, magnetic material definition, and magnetic boundary conditions, see the Low-Frequency Electromagnetic Analysis Guide. Magnetoelasticity in the Theory Reference describes the magnetic force strong coupling.
Table 2.28: Elements Used in Magneto-Structural Analyses
| Elements | Magnetic Formulation | Magnetic Force | Analysis Types | |
|---|---|---|---|---|
| Type | Coupling Method | |||
|
PLANE13 - 4-Node Coupled-Field Quadrilateral | Magnetic Vector Potential (AZ) |
Surface Maxwell or Volumetric Lorentz (enforced for conductors) | Weak |
Static Full Transient |
|
SOLID5 - 8-Node Coupled-Field Brick SOLID98 - 10-Node Coupled-Field Tetrahedron | Magnetic Scalar Potential (MAG) | Weak | Static | |
|
PLANE223 - 8-Node Coupled-Field Quadrilateral | Magnetic Vector Potential (AZ) |
Volumetric Maxwell or Volumetric Lorentz (applicable to models with current carrying conductors) | Strong |
Static Full Transient |
|
SOLID226 - 20-Node Coupled-Field Brick SOLID227 - 10-Node Coupled-Field Tetrahedron | Edge-Flux (AZ) | |||
PLANE223, SOLID226, and SOLID227 are considered current technology elements (see Current-Technology Elements in the Element Reference) and are the preferred elements for magneto-structural analysis. For these elements, the type of coupled magneto-structural analysis is determined by the KEYOPT(1) setting. The following table lists the available analysis options along with the magnetic materials or current carrying conductors they can be applied to. (Note, 2D analyses do not include the UZ degree of freedom.)
Table 2.29: Magneto-Structural Analyses
| KEYOPT(1) | Coupled Analysis | Degrees of Freedom | Physical Domain |
| 10001 | Structural-Magnetic | UX, UY, UZ, AZ |
Non-magnetic (for example, air, copper, aluminum) Soft Magnetic (for example, iron or steel) Hard Magnetic (permanent magnets) Stranded Conductor |
| 10101 | Structural-Electromagnetic | UX, UY, UZ, AZ, VOLT | Solid Conductor (for example, copper or aluminum) |
| 10201 | Structural-Stranded Coil | UX, UY, UZ, AZ, VOLT, EMF | Stranded Coil |
For the other elements, select a KEYOPT(1) setting that includes structural and magnetic degrees of freedom, and the electric degree of freedom if needed:
To perform a magneto-structural analysis using current technology coupled-field elements PLANE223, SOLID226, and SOLID227, follow this procedure:
Select a coupled-field element type that is appropriate for the analysis (see Table 2.28: Elements Used in Magneto-Structural Analyses) and set KEYOPT(1) to activate the degrees of freedom necessary to model the desired physical domain (see Table 2.29: Magneto-Structural Analyses).
See Modeling Elastic Air for suggestions on how to morph the magnetic air regions when using the structural-magnetic analysis option (KEYOPT(1) = 10001).
Use KEYOPT(8) to select the magnetic force calculation method. The Maxwell force option (KEYOPT(8) = 0) can be used to calculate the deformation of permeable magnetic solids and current-carrying conductors; the Lorentz force option (KEYOPT(8) = 1) can only be used in a magneto-structural analysis of current-carrying conductors.
Note that you cannot intermix the Maxwell and Lorentz force methods in adjacent magnetic domains. For example, if an air region surrounds a current carrying conductor that uses the Lorentz force option (KEYOPT(8) = 1), then the air region should also be assigned KEYOPT(8) = 1.
For a structural-electromagnetic analysis of current carrying solid conductors (KEYOPT(1) = 10101), use KEYOPT(5) to control the eddy currents and velocity effects.
Specify structural material properties. See the Structural Material Properties table in the PLANE223, SOLID226, and SOLID227 element descriptions for details.
Specify magnetic material properties:
For a structural-electromagnetic analysis (KEYOPT(1) = 10101), specify electrical resistivity as RSVX, RSVY, and RSVZ (MP).
For a structural-stranded coil analysis (KEYOPT(1) = 10201), specify the coil parameters as real constants for the element (R). For a detailed description of the coil parameter real constants, see Performing a 2D Stranded Coil Analysis (for a 2D analysis) and Performing a Stranded Coil Analysis (for a 3D analysis) in the Low-Frequency Electromagnetic Analysis Guide.
Apply structural, magnetic, and electric loads, initial conditions, and boundary conditions:
Structural loads, initial conditions, and boundary conditions include:
Displacement (UX, UY, UZ) (D and IC) Force (FX, FY, FZ) (F) Pressure (PRES) (SF or SFE) Force density (FORC) (BFE) Magnetic loads, initial conditions, and boundary conditions include magnetic degrees of freedom AZ (D and IC) and, in a structural-magnetic analysis (KEYOPT(1) = 10001), the electric current density JS (BFE). In a 3D magneto-structural analysis, you can apply a uniform magnetic field (DFLX).
For a structural-electromagnetic analysis (KEYOPT(1) = 10101) and a structural-stranded coil analysis (KEYOPT(1) = 100201), electrical loads, initial conditions, and boundary conditions include electric potential VOLT (D and IC) and electric current AMPS (F).
In a 2D structural-electromagnetic analysis, VOLT degrees of freedom must be coupled (CP,,VOLT).
In a structural-stranded coil analysis (KEYOPT(1) = 10201), couple VOLT and EMF degrees of freedom for each coil: CP,,VOLT and CP,,EMF.
Specify analysis type and solve:
Analysis type can be static or full transient.
Enable large-deflection effects (NLGEOM).
Specify convergence criteria for the magnetic and structural degrees of freedom (AZ and U) or forces (CSG and F) (CNVTOL).
The magneto-structural analysis is nonlinear and requires at least two iterations to obtain a converged solution.
For problems having convergence difficulties, activate the line-search capability (LNSRCH).
Post-process the structural and magnetic results:
Structural results include displacements (U), total strain (EPTO), elastic strain (EPEL), thermal strain (EPTH), plastic strain (EPPL), creep strain (EPCR), and stress (S). In an analysis with material or geometric nonlinearities, structural results include plastic yield stress (SEPL), accumulated equivalent plastic strain (EPEQ), accumulated equivalent creep strain (CREQ), plastic yielding (SRAT), and hydrostatic pressure (HPRES), and elastic strain energy (SENE).
Magnetic results include magnetic vector potential (AZ), magnetic flux density (B), magnetic flux intensity (H), conduction current density (JT), current density (JS), electromagnetic forces (FMAG), Joule heat generation rate (JHEAT), magnetic energy (UMAG), and magnetic co-energy (COEN).
Structural-electromagnetic analysis results also include the electric potential (VOLT), electric field intensity (EF), and conduction current density (JC).
Structural-stranded coil analysis results also include the electromotive force (EMF) and current (CURT).
The magnetic field, and therefore the magnetic forces acting on the deforming structure, change with the displacement of the structure. To take this change into account, the air region surrounding a solid magnetic material or current carrying conductor must be morphed, achieved by adding structural degrees of freedom (in addition to magnetic) and by assigning nominal elastic properties to the air elements.
To morph air regions, do the following:
Use the structural-magnetic analysis option (KEYOPT(1) = 10001) to model air regions. This adds structural degrees of freedom to the magnetic model of the air region, allowing the magnetic field (and forces) in the air domain to change following the deformation of the solid parts of the model.
Set KEYOPT(4) = 1 or 3 to apply the magnetic force only to element nodes connected to a structure, but not to the nodes interior to the air domain.
KEYOPT(4) = 1 is recommended for air elements with all nodes either constrained or connected to the structure, e.g., when a thin air gap is modelled using a single layer of elements without midside nodes. This KEYOPT(4) setting produces a symmetric matrix.
KEYOPT(4) =3 is recommended for air elements with free nodes, that is, nodes not attached to the structure and not constrained. Using this option will improve convergence of a nonlinear analysis and result accuracy of a linear perturbation analysis. This option produces an unsymmetric matrix. The unsymmetric modal solver (MODOPT,UNSYM) should be used in the downstream linear perturbation modal analysis.
For computational efficiency, use KEYOPT(4) = 1 or 3 only for the air elements attached to a structure and KEYOPT(4) = 2 for the rest of the air region.
Assign a small elastic stiffness and a zero Poisson's ratio to the elastic air elements.
Enable large-deflection effects (NLGEOM,ON).
Rigidly fix the exterior of the air region by constraining structural displacements.
A magneto-structural analysis involving elastic air regions should be limited to small movement of the structure; that is, movement up to a point where air mesh distortion remains acceptable.
This example demonstrates a static magneto-structural analysis of a ferromagnetic beam suspended above a permanent magnet.
The following topics are available:
A beam made of material with high magnetic permeability (µr = 105) is suspended above the permanent magnet with coercive field Hc = 2.5e6 A/m.
The beam, the permanent magnet, and the surrounding air are modeled using the structural-magnetic analysis option (KEYOPT(1) = 10001) of a 2D coupled-field solid element, PLANE223:
The force-calculation method is set to Maxwell (KEYOPT(8) = 0), the only option available for ferromagnetic solids. The air domain is assigned a negligible elasticity modulus and a zero Poisson’s ratio to allow the air mesh to deform. KEYOPT(4) is set to 1 for the air domain to ensure that the magnetic force is applied to the air-solid interface and not to the nodes interior to the air domain.
The permanent magnet is fully constrained, and the beam is clamped at both ends. The outer edge of the elastic air domain is constrained. Flux-parallel magnetic boundary conditions are applied to the outer boundary of the air domain by setting the AZ degree of freedom to zero.
A static analysis is performed to determine the deformation of the beam due to the magnetic force. Large-deflection effects are enabled (NLGEOM,ON.
The simulation results are presented in the form of a magnetic flux (B) vector plot and a contour plot of the total displacement (U):
/title, Double-clamped ferromagnetic beam above a magnet /prep7 !! Element types et,1,223,10001 ! 2D magneto-structural solid for ferroelastic beam et,2,223,10001 ! 2D magneto-structural solid for "elastic" air keyopt,2,4,1 ! magnetic force applied to the air-structure interface !! Material properties ! "elastic" air mp,ex,1,1e-3 ! Young's modulus, Pa mp,nuxy,1,0 ! Poisson's ratio mp,murx,1,1 ! relative magnetic permeability ! ferroelastic beam mp,ex,2,10e7 ! Young's modulus, Pa mp,nuxy,2,0.3 ! Poisson's ratio mp,murx,2,100000 ! relative magnetic permeability ! permanent magnet mp,ex,3,10e10 ! Young's modulus, Pa mp,nuxy,3,0.3 ! Poisson's ratio mp,mgyy,3,2.5e6 ! coercive force, A/m mp,murx,3,5.3 ! relative magnetic permeability !! Dimensions, m pm_x=1e-3 ! permanent magnet pm_y=3e-3 fm_x=20e-3 ! ferromagnetic core fm_y=1e-3 air_gap_y=3e-3 ! air domain air_o=4e-3 mshmid,2 ! mesh without midside nodes !! Solid model and mesh ! create and mesh permanent magnet rectng,-pm_x/2,pm_x/2,0,pm_y type,1 mat,3 esize,pm_x/3 amesh,1 ! create and mesh ferromagnetic core rectng,-fm_x/2,fm_x/2, pm_y+air_gap_y,pm_y+air_gap_y+fm_y type,1 mat,2 esize,fm_y/2 amesh,2 ! create air domain rectng,-fm_x/2-air_o,fm_x/2+air_o, -pm_x/2-air_o,pm_y+air_gap_y+fm_y+air_o aovlap,all ! mesh air domain type,2 mat,1 msha,1,2D ! triangle mesh for the air region esize,air_o amesh,4 /pnum,mat,1 /number,1 eplot !! Boundary conditions ! fix magnet esel,s,mat,,3 nsle d,all,ux,0 d,all,uy,0 alls ! fix ferromagnetic core ends nsel,s,loc,x,-fm_x/2 nsel,a,loc,x,fm_x/2 esln esel,r,mat,,2 nsle,r d,all,ux,0 d,all,uy,0 alls ! fix outer edge of the air region nsel,s,ext d,all,ux,0 d,all,uy,0 alls ! flux-parallel magnetic boundary conditions on the outer edge of the air box nsel,s,ext d,all,az,0 alls,all fini !! solution /solu antype,static ! static analysis nlgeom,on ! large deflection enabled cnvtol,f,1,1e-1 ! force convergence tolerance outres,all,all solve fini /post1 set,last,last /title, Magnetic flux /vscale,1,1.2,0 plvect,b,,,,vect,node,on,0 /title, Mechanical displacement plnsol,u,sum fini
This example demonstrates a transient structural-electromagnetic analysis of a wire with skin effect.
The following topics are available:
This figure shows the finite element discretization of a quarter symmetry model of the wire with surrounding air:
The wire is modeled using the structural-electromagnetic analysis option (KEYOPT(1) = 10101) of the 3D coupled-field solid element, SOLID226. The force calculation method is set to Lorentz (KEYOPT(8) = 1) for the wire, although the Maxwell force calculation option (KEYOPT(8) = 0) is also applicable to this model.
The surrounding air domain is modelled with the structural-magnetic analysis option (KEYOPT(1) = 10001) of SOLID226. The air elements are assigned a negligible elasticity modulus and a zero Poisson’s ratio to allow the air mesh to deform. KEYOPT(4) is set to 1 for the air elements to ensure that the magnetic force is applied only to the air-solid interface. Although the air element does not carry electric current, KEYOPT(8) is set to 1 for all air elements to consistently use the Lorentz force method across the model.
The wire is constrained in the axial direction and on the symmetry planes to ensure radial deformation only. The outer boundary of the elastic air domain is constrained as well. Flux-parallel magnetic boundary conditions are applied to the outer boundary of the air domain by setting the edge-flux degree of freedom (AZ) to zero.
A sinusoidal current is applied to the wire using the CIRCU124 element type with the independent current source option (KEYOPT(1) = 3) and the sinusoidal load option (KEYOPT(2) = 1).
A transient analysis is performed for four milliseconds to determine the deformation and stress in the wire. Large-deflection effects are enabled (NLGEOM,ON).
The applied sinusoidal current load and the resulting current density, magnetic flux, and von Mises stress at the edge of the wire are shown in the next four figures.
The distribution of calculated electrical, magnetic, and mechanical quantities in the wire and surrounding air are presented below at simulation time = 3.142e-3 s.
The fast change in the magnetic field produces a skin effect with the current density (J) concentrated near the surface of the wire as shown in Figure 2.76: Electric Current Density . The magnetic flux (B) distribution in and around the wire is shown in Figure 2.77: Magnetic Flux Density. The resulting Lorentz (J x B) force acts in the radial direction, towards the center of the wire (Figure 2.78: Magnetic Force) and produces the deformation and stress shown in Figure 2.79: Mechanical Deformation and Figure 2.80: Von Mises Stress .
/title, Skin effect in an elastic wire /prep7 et,1,226,10001 ! structural-magnetic brick for "elastic" air keyop,1,4,1 ! magnetic force applied to the air-structure interface !keyop,1,8,0 ! Maxwell force can be used instead keyop,1,8,1 ! Lorentz force et,2,226,10101 ! structural-electromagnetic brick !keyop,1,8,0 ! Maxwell force can be used instead keyop,2,8,1 ! Lorentz force et,3,124,3,1 ! independent current source, sin load !! Material properties ! "elastic" air mp,ex,1,1e-3 ! Young's modulus, Pa mp,prxy,1,0.0 ! Poisson's ratio mp,murx,1,1 ! relative magnetic permeability ! wire mp,ex,2,1e8 ! Young's modulus, Pa mp,prxy,2,0.3 ! Poisson's ratio mp,murx,2,1 ! relative magnetic permeability mp,rsvx,2,2e-8 ! electrical resistivity, Ohm_m n,1, ! reserve node for circuit connection !! Solid model and mesh ! wire cylinder,,0.1,0,0.01,0,90 ! air cylinder,0.1,0.2,0,0.01,0,90 nummrg,kp esize,0.005 ! "skin depth" type,2 mat,2 vmesh,1 type,1 mat,1 vmesh,2 /pnum,mat,1 /number,1 eplot !! Boundary conditions csys,1 ! cylindrical coordinate system ! structural BCs nsel,s,loc,z,0 nsel,a,loc,z,0.01 d,all,uz nsel,s,loc,x,0 d,all,ux d,all,uy d,all,uz nsel,s,loc,y,0 d,all,uy nsel,s,loc,y,90 d,all,ux nsel,all ! flux parallel magnetic BCs nsel,s,loc,z,0 nsel,a,loc,z,0.01 nsel,a,loc,x,0.2 d,all,az,0 nsel,all ! Ground voltage nsel,s,loc,z,0 cp,1,volt,all ng=ndnext(0) nsel,all d,ng,volt,0 ! Couple voltage nsel,s,loc,z,0.01 cp,2,volt,all nd=ndnext(0) nsel,all ! Circu124 current source type,3 pi=acos(-1) frq=1000/(2*pi) Ipeak=1e4 r,1,Ipeak,Ipeak,frq,,-90 real,1 e,1,nd ! create circuit element d,1,volt,0 ! ground current source circuit *get,emax,elem,0,num,max fini /solu antype,trans ! transient analysis time,4e-3 ! simulation time, s deltim,1e-4 ! time step,s kbc,1 ! stepped load nlgeom,on ! large-deflection effects enabled outres,all,all solve fini /post26 /axlab,x,TIME (s) /axlab,y,Applied Electric Current, A esol,2,emax,,smisc,2,CURRENT ! current in the circuit plvar,2 nsel,s,loc,x,0.1 nsel,r,loc,y,45 nsel,r,loc,z,0 n26=ndnext(0) esln esel,r,mat,,2 /axlab,y,Electric Current Density, A/m**2 esol,3,elnext(0),n26,jc,sum,JC plvar,3 /axlab,y,Magnetic Flux Density, tesla esol,4,elnext(0),n26,b,sum,B plvar,4 /axlab,y,Von Mises Stress, Pa esol,5,elnext(0),n26,s,eqv,SEQV plvar,5 alls fini /post1 set,last,last /title, Electric current density plvect,jc, , , ,vect,elem,on,0 /title, Magnetic flux density plvect,b, , , ,vect,elem,on,0 /title, Magnetic (Lorentz) force plvect,fmag, , , ,vect,elem,on,0 /title, Mechanical displacement plnsol,u,sum /title, Von Mises Stress plnsol,s,eqv fini
Another magneto-structural analysis example is found in the Mechanical APDL Verification Manual: