ProductsAbaqus/StandardAbaqus/ExplicitAbaqus/CAE
Element types
Stress/displacement elements
- STRI3(S)
3-node triangular facet thin shell
- S3
3-node triangular general-purpose shell, finite membrane strains (identical to element S3R)
- S3R
3-node triangular general-purpose shell, finite membrane strains (identical to element S3)
- S3RS(E)
3-node triangular shell, small membrane strains
- STRI65(S)
6-node triangular thin shell, using five degrees of freedom per node
- S4
4-node general-purpose shell, finite membrane strains
- S4R
4-node general-purpose shell, reduced integration with hourglass control, finite membrane strains
- S4RS(E)
4-node, reduced integration, shell with hourglass control, small membrane strains
- S4RSW(E)
4-node, reduced integration, shell with hourglass control, small membrane strains, warping considered in small-strain formulation
- S4R5(S)
4-node thin shell, reduced integration with hourglass control, using five degrees of freedom per node
- S8R(S)
8-node doubly curved thick shell, reduced integration
- S8R5(S)
8-node doubly curved thin shell, reduced integration, using five degrees of freedom per node
- S9R5(S)
9-node doubly curved thin shell, reduced integration, using five degrees of freedom per node
Active degrees of freedom
1, 2, 3, 4, 5, 6 for STRI3, S3R, S3RS, S4, S4R, S4RS, S4RSW, S8R
1, 2, 3 and two in-surface rotations for STRI65, S4R5, S8R5, S9R5 at most nodes
1, 2, 3, 4, 5, 6 for STRI65, S4R5, S8R5, S9R5 at any node that
has a boundary condition on a rotational degree of freedom;
is involved in a multi-point constraint that uses rotational degrees of freedom;
is attached to a beam or to a shell element that uses six degrees of freedom at all nodes (such as S4R, S8R, STRI3, etc.);
is a point where different elements have different surface normals (user-specified normal definitions or normal definitions created by Abaqus because the surface is folded); or
is loaded with moments.
Additional solution variables
Element type S8R5 has three displacement and two rotation variables at an internally generated midbody node.
Heat transfer elements
- DS3(S)
3-node triangular shell
- DS4(S)
4-node quadrilateral shell
- DS6(S)
6-node triangular shell
- DS8(S)
8-node quadrilateral shell
Additional solution variables
None.
Coupled temperature-displacement elements
- S3T(S)
3-node triangular general-purpose shell, finite membrane strains, bilinear temperature in the shell surface (identical to element S3RT)
- S3RT
3-node triangular general-purpose shell, finite membrane strains, bilinear temperature in the shell surface (for Abaqus/Standard it is identical to element S3T )
- S4T(S)
4-node general-purpose shell, finite membrane strains, bilinear temperature in the shell surface
- S4RT
4-node general-purpose shell, reduced integration with hourglass control, finite membrane strains, bilinear temperature in the shell surface
- S8RT(S)
8-node thick shell, biquadratic displacement, bilinear temperature in the shell surface
Active degrees of freedom
1, 2, 3, 4, 5, 6 at all nodes
11, 12, 13, etc. (temperatures through the thickness as described in Choosing a shell element) at all nodes for S3T, S3RT, S4T, and S4RT; and at the corner nodes only for S8RT
Additional solution variables
None.
Nodal coordinates required
and, optionally for shells with displacement degrees of freedom in Abaqus/Standard, , the direction cosines of the shell normal at the node.
Element property definition
Input File Usage
Use either of the following options for stress/displacement elements:
SHELL SECTION
SHELL GENERAL SECTION
Use the following option for heat transfer or coupled temperature-displacement elements:
SHELL SECTION
In addition, use the following option for variable thickness shells:
NODAL THICKNESS
Abaqus/CAE Usage
Property module: Create Section: select Shell as the section Category and Homogeneous or Composite as the section Type
Element-based loading
Distributed loads
Distributed loads are available for all elements with displacement degrees of freedom. They are specified as described in Distributed loads.
Body forces, centrifugal loads, and Coriolis forces must be given as force per unit area if the equivalent section properties are specified directly as part of the general shell section definition.
*dload
- Load ID (*DLOAD): BX
- Body force
- FL−3
Body force (give magnitude as force per unit volume) in the global X-direction.
- Load ID (*DLOAD): BY
- Body force
- FL−3
Body force (give magnitude as force per unit volume) in the global Y-direction.
- Load ID (*DLOAD): BZ
- Body force
- FL−3
Body force (give magnitude as force per unit volume) in the global Z-direction.
- Load ID (*DLOAD): BXNU
- Body force
- FL−3
Nonuniform body force (give magnitude as force per unit volume) in the global X-direction, with magnitude supplied via user subroutine DLOAD in Abaqus/Standard and VDLOAD in Abaqus/Explicit.
- Load ID (*DLOAD): BYNU
- Body force
- FL−3
Nonuniform body force (give magnitude as force per unit volume) in the global Y-direction, with magnitude supplied via user subroutine DLOAD in Abaqus/Standard and VDLOAD in Abaqus/Explicit.
- Load ID (*DLOAD): BZNU
- Body force
- FL−3
Nonuniform body force (give magnitude as force per unit volume) in the global Z-direction, with magnitude supplied via user subroutine DLOAD in Abaqus/Standard and VDLOAD in Abaqus/Explicit.
- Load ID (*DLOAD): CENT(S)
- Not supported
- FL−4 (ML−3T−2)
Centrifugal load (magnitude defined as , where is the mass density and is the angular speed).
- Load ID (*DLOAD): CENTRIF(S)
- Rotational body force
- T−2
Centrifugal load (magnitude is input as , where is the angular speed).
- Load ID (*DLOAD): CORIO(S)
- Coriolis force
- FL−4T (ML−3T−1)
Coriolis force (magnitude input , where is the mass density and is the angular speed). The load stiffness due to Coriolis loading is not accounted for in direct steady-state dynamics analysis.
- Load ID (*DLOAD): EDLDn
- Shell edge load
- FL−1
General traction on edge n.
- Load ID (*DLOAD): EDLDnNU(S)
- Not supported
- FL−1
Nonuniform general traction on edge n with magnitude and direction supplied via user subroutine UTRACLOAD.
- Load ID (*DLOAD): EDMOMn
- Shell edge load
- F
Moment on edge n.
- Load ID (*DLOAD): EDMOMnNU(S)
- Not supported
- F
Nonuniform moment on edge n with magnitude supplied via user subroutine UTRACLOAD.
- Load ID (*DLOAD): EDNORn
- Shell edge load
- FL−1
Normal traction on edge n.
- Load ID (*DLOAD): EDNORnNU(S)
- Not supported
- FL−1
Nonuniform normal traction on edge n with magnitude supplied via user subroutine UTRACLOAD.
- Load ID (*DLOAD): EDSHRn
- Shell edge load
- FL−1
Shear traction on edge n.
- Load ID (*DLOAD): EDSHRnNU(S)
- Not supported
- FL−1
Nonuniform shear traction on edge n with magnitude supplied via user subroutine UTRACLOAD.
- Load ID (*DLOAD): EDTRAn
- Shell edge load
- FL−1
Transverse traction on edge n.
- Load ID (*DLOAD): EDTRAnNU(S)
- Not supported
- FL−1
Nonuniform transverse traction on edge n with magnitude supplied via user subroutine UTRACLOAD.
- Load ID (*DLOAD): GRAV
- Gravity
- LT−2
Gravity loading in a specified direction (magnitude is input as acceleration).
- Load ID (*DLOAD): HP(S)
- Not supported
- FL−2
Hydrostatic pressure applied to the element reference surface and linear in global Z. The pressure is positive in the direction of the positive element normal.
- Load ID (*DLOAD): P
- Pressure
- FL−2
Pressure applied to the element reference surface. The pressure is positive in the direction of the positive element normal.
- Load ID (*DLOAD): PNU
- Not supported
- FL−2
Nonuniform pressure applied to the element reference surface with magnitude supplied via user subroutine DLOAD in Abaqus/Standard and VDLOAD in Abaqus/Explicit. The pressure is positive in the direction of the positive element normal.
- Load ID (*DLOAD): ROTA(S)
- Rotational body force
- T−2
Rotary acceleration load (magnitude is input as , where is the rotary acceleration).
- Load ID (*DLOAD): ROTDYNF(S)
- Not supported
- T−1
Rotordynamic load (magnitude is input as , where is the angular velocity).
- Load ID (*DLOAD): SBF(E)
- Not supported
- FL−5T
Stagnation body force in global X-, Y-, and Z-directions.
- Load ID (*DLOAD): SP(E)
- Not supported
- FL−4T2
Stagnation pressure applied to the element reference surface.
- Load ID (*DLOAD): TRSHR
- Surface traction
- FL−2
Shear traction on the element reference surface.
- Load ID (*DLOAD): TRSHRNU(S)
- Not supported
- FL−2
Nonuniform shear traction on the element reference surface with magnitude and direction supplied via user subroutine UTRACLOAD.
- Load ID (*DLOAD): TRVEC
- Surface traction
- FL−2
General traction on the element reference surface.
- Load ID (*DLOAD): TRVECNU(S)
- Not supported
- FL−2
Nonuniform general traction on the element reference surface with magnitude and direction supplied via user subroutine UTRACLOAD.
- Load ID (*DLOAD): VBF(E)
- Not supported
- FL−4T
Viscous body force in global X-, Y-, and Z-directions.
- Load ID (*DLOAD): VP(E)
- Not supported
- FL−3T
Viscous surface pressure. The viscous pressure is proportional to the velocity normal to the element face and opposing the motion.
Foundations
Foundations are available for Abaqus/Standard elements with displacement degrees of freedom. They are specified as described in Element foundations.
*foundation
- Load ID (*FOUNDATION): F(S)
- Elastic foundation
- FL−3
Elastic foundation in the direction of the shell normal.
Distributed heat fluxes
Distributed heat fluxes are available for elements with temperature degrees of freedom. They are specified as described in Thermal loads.
*dflux
- Load ID (*DFLUX): BF(S)
- Body heat flux
- JL−3 T−1
Body heat flux per unit volume.
- Load ID (*DFLUX): BFNU(S)
- Body heat flux
- JL−3 T−1
Nonuniform body heat flux per unit volume with magnitude supplied via user subroutine DFLUX.
- Load ID (*DFLUX): SNEG(S)
- Surface heat flux
- JL−2 T−1
Surface heat flux per unit area into the bottom face of the element.
- Load ID (*DFLUX): SPOS(S)
- Surface heat flux
- JL−2 T−1
Surface heat flux per unit area into the top face of the element.
- Load ID (*DFLUX): SNEGNU(S)
- Not supported
- JL−2 T−1
Nonuniform surface heat flux per unit area into the bottom face of the element with magnitude supplied via user subroutine DFLUX.
- Load ID (*DFLUX): SPOSNU(S)
- Not supported
- JL−2 T−1
Nonuniform surface heat flux per unit area into the top face of the element with magnitude supplied via user subroutine DFLUX.
Film conditions
Film conditions are available for elements with temperature degrees of freedom. They are specified as described in Thermal loads.
*film
- Load ID (*FILM): FNEG(S)
- Surface film condition
- JL−2 T−1−1
Film coefficient and sink temperature (units of ) provided on the bottom face of the element.
- Load ID (*FILM): FPOS(S)
- Surface film condition
- JL−2 T−1−1
Film coefficient and sink temperature (units of ) provided on the top face of the element.
- Load ID (*FILM): FNEGNU(S)
- Not supported
- JL−2 T−1−1
Nonuniform film coefficient and sink temperature (units of ) provided on the bottom face of the element with magnitude supplied via user subroutine FILM.
- Load ID (*FILM): FPOSNU(S)
- Not supported
- JL−2 T−1−1
Nonuniform film coefficient and sink temperature (units of ) provided on the top face of the element with magnitude supplied via user subroutine FILM.
Radiation types
Radiation conditions are available for elements with temperature degrees of freedom. They are specified as described in Thermal loads.
*radiate
- Load ID (*RADIATE): RNEG(S)
- Surface radiation
- Dimensionless
Emissivity and sink temperature (units of ) provided for the bottom face of the shell.
- Load ID (*RADIATE): RPOS(S)
- Surface radiation
- Dimensionless
Emissivity and sink temperature (units of ) provided for the top face of the shell.
Surface-based loading
Distributed loads
Surface-based distributed loads are available for all elements with displacement degrees of freedom. They are specified as described in Distributed loads.
*dsload
- Load ID (*DSLOAD): EDLD
- Shell edge load
- FL−1
General traction on edge-based surface.
- Load ID (*DSLOAD): EDLDNU(S)
- Shell edge load
- FL−1
Nonuniform general traction on edge-based surface with magnitude and direction supplied via user subroutine UTRACLOAD.
- Load ID (*DSLOAD): EDMOM
- Shell edge load
- F
Moment on edge-based surface.
- Load ID (*DSLOAD): EDMOMNU(S)
- Shell edge load
- F
Nonuniform moment on edge-based surface with magnitude supplied via user subroutine UTRACLOAD.
- Load ID (*DSLOAD): EDNOR
- Shell edge load
- FL−1
Normal traction on edge-based surface.
- Load ID (*DSLOAD): EDNORNU(S)
- Shell edge load
- FL−1
Nonuniform normal traction on edge-based surface with magnitude supplied via user subroutine UTRACLOAD.
- Load ID (*DSLOAD): EDSHR
- Shell edge load
- FL−1
Shear traction on edge-based surface.
- Load ID (*DSLOAD): EDSHRNU(S)
- Shell edge load
- FL−1
Nonuniform shear traction on edge-based surface with magnitude supplied via user subroutine UTRACLOAD.
- Load ID (*DSLOAD): EDTRA
- Shell edge load
- FL−1
Transverse traction on edge-based surface.
- Load ID (*DSLOAD): EDTRANU(S)
- Shell edge load
- FL−1
Nonuniform transverse traction on edge-based surface with magnitude supplied via user subroutine UTRACLOAD.
- Load ID (*DSLOAD): HP(S)
- Pressure
- FL−2
Hydrostatic pressure on the element reference surface and linear in global Z. The pressure is positive in the direction opposite to the surface normal.
- Load ID (*DSLOAD): P
- Pressure
- FL−2
Pressure on the element reference surface. The pressure is positive in the direction opposite to the surface normal.
- Load ID (*DSLOAD): PNU
- Pressure
- FL−2
Nonuniform pressure on the element reference surface with magnitude supplied via user subroutine DLOAD in Abaqus/Standard and VDLOAD in Abaqus/Explicit. The pressure is positive in the direction opposite to the surface normal.
- Load ID (*DSLOAD): SP(E)
- Pressure
- FL−4T2
Stagnation pressure applied to the element reference surface.
- Load ID (*DSLOAD): TRSHR
- Surface traction
- FL−2
Shear traction on the element reference surface.
- Load ID (*DSLOAD): TRSHRNU(S)
- Surface traction
- FL−2
Nonuniform shear traction on the element reference surface with magnitude and direction supplied via user subroutine UTRACLOAD.
- Load ID (*DSLOAD): TRVEC
- Surface traction
- FL−2
General traction on the element reference surface.
- Load ID (*DSLOAD): TRVECNU(S)
- Surface traction
- FL−2
Nonuniform general traction on the element reference surface with magnitude and direction supplied via user subroutine UTRACLOAD.
- Load ID (*DSLOAD): VP(E)
- Pressure
- FL−3T
Viscous surface pressure. The viscous pressure is proportional to the velocity normal to the element face and opposing the motion.
Distributed heat fluxes
Surface-based distributed heat fluxes are available for elements with temperature degrees of freedom. They are specified as described in Thermal loads.
*dsflux
- Load ID (*DSFLUX): S(S)
- Surface heat flux
- JL−2 T−1
Surface heat flux per unit area into the element surface.
- Load ID (*DSFLUX): SNU(S)
- Surface heat flux
- JL−2 T−1
Nonuniform surface heat flux per unit area into the element surface with magnitude supplied via user subroutine DFLUX.
Film conditions
Surface-based film conditions are available for elements with temperature degrees of freedom. They are specified as described in Thermal loads.
*sfilm
- Load ID (*SFILM): F(S)
- Surface film condition
- JL−2 T−1−1
Film coefficient and sink temperature (units of ) provided on the element surface.
- Load ID (*SFILM): FNU(S)
- Surface film condition
- JL−2 T−1−1
Nonuniform film coefficient and sink temperature (units of ) provided on the element surface with magnitude supplied via user subroutine FILM.
Radiation types
Surface-based radiation conditions are available for elements with temperature degrees of freedom. They are specified as described in Thermal loads.
*sradiate
- Load ID (*SRADIATE): R(S)
- Surface radiation
- Dimensionless
Emissivity and sink temperature (units of ) provided for the element surface.
Element output
If a local coordinate system is not assigned to the element, the stress/strain components, as well as the section forces/strains, are in the default directions on the surface defined by the convention given in Conventions. If a local coordinate system is assigned to the element through the section definition (Orientations), the stress/strain components and the section forces/strains are in the surface directions defined by the local coordinate system. In large-displacement problems with elements that allow finite membrane strains in Abaqus/Standard and in all problems in Abaqus/Explicit, the local directions defined in the reference configuration are rotated into the current configuration by the average material rotation.
Stress, strain, and other tensor components
Stress and other tensors (including strain tensors) are available for elements with displacement degrees of freedom. All tensors have the same components. For example, the stress components are as follows:
- S11
Local direct stress.
- S22
Local direct stress.
- S12
Local shear stress.
Section forces, moments, and transverse shear forces
Available for elements with displacement degrees of freedom.
- SF1
Direct membrane force per unit width in local 1-direction.
- SF2
Direct membrane force per unit width in local 2-direction.
- SF3
Shear membrane force per unit width in local 1–2 plane.
- SF4
Transverse shear force per unit width in local 1-direction (available only for S3/S3R, S3RS, S4, S4R, S4RS, S4RSW, S8R, and S8RT).
- SF5
Transverse shear force per unit width in local 2-direction (available only for S3/S3R, S3RS, S4, S4R, S4RS, S4RSW, S8R, and S8RT).
- SM1
Bending moment force per unit width about local 2-axis.
- SM2
Bending moment force per unit width about local 1-axis.
- SM3
Twisting moment force per unit width in local 1–2 plane.
The section force and moment resultants per unit length in the normal basis directions in a given shell section of thickness h can be defined on this basis as
where is the offset of the reference surface from the midsurface. The section force SF6, which is the integral of through the shell thickness, is reported only for finite-strain shell elements and is zero because of the plane stress constitutive assumption. The total number of attributes written to the results file for finite-strain shell elements is 9; SF6 is the sixth attribute.
Average section stresses
Available for elements with displacement degrees of freedom.
- SSAVG1
Average membrane stress in local 1-direction.
- SSAVG2
Average membrane stress in local 2-direction.
- SSAVG3
Average membrane stress in local 1–2 plane.
- SSAVG4
Average transverse shear stress in local 1-direction.
- SSAVG5
Average transverse shear stress in local 2-direction.
The average section stresses are defined as
where h is the current section thickness.
Section strains, curvatures, and transverse shear strains
Available for elements with displacement degrees of freedom.
- SE1
Direct membrane strain in local 1-direction.
- SE2
Direct membrane strain in local 2-direction.
- SE3
Shear membrane strain in local 1–2 plane.
- SE4
Transverse shear strain in the local 1-direction (available only for S3/S3R, S3RS, S4, S4R, S4RS, S4RSW, S8R, and S8RT).
- SE5
Transverse shear strain in the local 2-direction (available only for S3/S3R, S3RS, S4, S4R, S4RS, S4RSW, S8R, and S8RT).
- SE6
Strain in the thickness direction (available only for S3/S3R, S3RS, S4, S4R, S4RS, and S4RSW).
- SK1
Curvature change about local 2-axis.
- SK2
Curvature change about local 1-axis.
- SK3
Surface twist in local 1–2 plane.
The local directions are defined in About shell elements.
Shell thickness
- STH
Shell thickness, which is the current section thickness for S3/S3R, S3RS, S4, S4R, S4RS, and S4RSW elements.
Transverse shear stress estimates
Available for S3/S3R, S3RS, S4, S4R, S4RS, S4RSW, S8R, and S8RT elements.
- TSHR13
13-component of transverse shear stress.
- TSHR23
23-component of transverse shear stress.
Estimates of the transverse shear stresses are available at section integration points as output variables TSHR13 or TSHR23 for both Simpson's rule and Gauss quadrature. For Simpson's rule output of variables TSHR13 or TSHR23 should be requested at nondefault section points, since the default output is at section point 1 of the shell section where the transverse shear stresses vanish. For the small-strain elements in Abaqus/Explicit, transverse shear stress distributions are assumed constant for non-composite sections and piecewise constant for composite sections; therefore, transverse shear stresses at integration points should be interpreted accordingly. For element type S4 the transverse shear calculation is performed at the center of the element and assumed constant over the element. Hence, transverse shear strain, force, and stress will not vary over the area of the element. For numerically integrated shell sections (with the exception of small-strain shells in Abaqus/Explicit), estimates of the interlaminar shear stresses in composite sections—i.e., the transverse shear stresses at the interface between two composite layers—can be obtained only by using Simpson's rule. With Gauss quadrature no section integration point exists at the interface between composite layers. Unlike the S11, S22, and S12 in-plane stress components, transverse shear stress components TSHR13 and TSHR23 are not calculated from the constitutive behavior at points through the shell section. They are estimated by matching the elastic strain energy associated with shear deformation of the shell section with that based on piecewise quadratic variation of the transverse shear stress across the section, under conditions of bending about one axis (see Transverse shear stiffness in composite shells and offsets from the midsurface). Therefore, interlaminar shear stress calculation is supported only when the elastic material model is used for each layer of the shell section. If you specify the transverse shear stiffness values, interlaminar shear stress output is not available.
Heat flux components
Available for elements with temperature degrees of freedom.
- HFL1
Heat flux in local 1-direction.
- HFL2
Heat flux in local 2-direction.
- HFL3
Heat flux in local 3-direction.
Node ordering on elements
Numbering of integration points for output
Stress/displacement analysis
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