Three-Dimensional Conventional Shell Element Library

This section provides a reference to the three-dimensional shell elements available in Abaqus/Standard and Abaqus/Explicit.

This page discusses:

 

See Also
About Shell Elements
Choosing a Shell Element
*NODAL THICKNESS
*SHELL GENERAL SECTION
*SHELL SECTION

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

Active Degrees of Freedom

11, 12, etc. (temperatures through the thickness as described in Choosing a Shell Element)

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

X,Y,Z and, optionally for shells with displacement degrees of freedom in Abaqus/Standard, Nx,Ny,Nz, the direction cosines of the shell normal at the node.

Element Property Definition

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
  1. Load ID (*DLOAD): BX
  2. FL−3

  3. Body force (give magnitude as force per unit volume) in the global X-direction.

  1. Load ID (*DLOAD): BY
  2. FL−3

  3. Body force (give magnitude as force per unit volume) in the global Y-direction.

  1. Load ID (*DLOAD): BZ
  2. FL−3

  3. Body force (give magnitude as force per unit volume) in the global Z-direction.

  1. Load ID (*DLOAD): BXNU
  2. FL−3

  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.

  1. Load ID (*DLOAD): BYNU
  2. FL−3

  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.

  1. Load ID (*DLOAD): BZNU
  2. FL−3

  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.

  1. Load ID (*DLOAD): CENT(S)
  2. FL−4 (ML−3T−2)

  3. Centrifugal load (magnitude defined as ρ⁢ω2, where ρ is the mass density and ω is the angular speed).

  1. Load ID (*DLOAD): CENTRIF(S)
  2. T−2

  3. Centrifugal load (magnitude is input as ω2, where ω is the angular speed).

  1. Load ID (*DLOAD): CORIO(S)
  2. FL−4T (ML−3T−1)

  3. Coriolis force (magnitude input ρ⁢ω, where ρ is the mass density and ω is the angular speed). The load stiffness due to Coriolis loading is not accounted for in direct steady-state dynamics analysis.

  1. Load ID (*DLOAD): EDLDn
  2. FL−1

  3. General traction on edge n.

  1. Load ID (*DLOAD): EDLDnNU(S)
  2. FL−1

  3. Nonuniform general traction on edge n with magnitude and direction supplied via user subroutine UTRACLOAD.

  1. Load ID (*DLOAD): EDMOMn
  2. F

  3. Moment on edge n.

  1. Load ID (*DLOAD): EDMOMnNU(S)
  2. F

  3. Nonuniform moment on edge n with magnitude supplied via user subroutine UTRACLOAD.

  1. Load ID (*DLOAD): EDNORn
  2. FL−1

  3. Normal traction on edge n.

  1. Load ID (*DLOAD): EDNORnNU(S)
  2. FL−1

  3. Nonuniform normal traction on edge n with magnitude supplied via user subroutine UTRACLOAD.

  1. Load ID (*DLOAD): EDSHRn
  2. FL−1

  3. Shear traction on edge n.

  1. Load ID (*DLOAD): EDSHRnNU(S)
  2. FL−1

  3. Nonuniform shear traction on edge n with magnitude supplied via user subroutine UTRACLOAD.

  1. Load ID (*DLOAD): EDTRAn
  2. FL−1

  3. Transverse traction on edge n.

  1. Load ID (*DLOAD): EDTRAnNU(S)
  2. FL−1

  3. Nonuniform transverse traction on edge n with magnitude supplied via user subroutine UTRACLOAD.

  1. Load ID (*DLOAD): GRAV
  2. LT−2

  3. Gravity loading in a specified direction (magnitude is input as acceleration).

  1. Load ID (*DLOAD): HP(S)
  2. FL−2

  3. 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.

  1. Load ID (*DLOAD): P
  2. FL−2

  3. Pressure applied to the element reference surface. The pressure is positive in the direction of the positive element normal.

  1. Load ID (*DLOAD): PNU
  2. FL−2

  3. 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.

  1. Load ID (*DLOAD): ROTA(S)
  2. T−2

  3. Rotary acceleration load (magnitude is input as α, where α is the rotary acceleration).

  1. Load ID (*DLOAD): ROTDYNF(S)
  2. T−1

  3. Rotordynamic load (magnitude is input as ω, where ω is the angular velocity).

  1. Load ID (*DLOAD): SBF(E)
  2. FL−5T

  3. Stagnation body force in global X-, Y-, and Z-directions.

  1. Load ID (*DLOAD): SP(E)
  2. FL−4T2

  3. Stagnation pressure applied to the element reference surface.

  1. Load ID (*DLOAD): TRSHR
  2. FL−2

  3. Shear traction on the element reference surface.

  1. Load ID (*DLOAD): TRSHRNU(S)
  2. FL−2

  3. Nonuniform shear traction on the element reference surface with magnitude and direction supplied via user subroutine UTRACLOAD.

  1. Load ID (*DLOAD): TRVEC
  2. FL−2

  3. General traction on the element reference surface.

  1. Load ID (*DLOAD): TRVECNU(S)
  2. FL−2

  3. Nonuniform general traction on the element reference surface with magnitude and direction supplied via user subroutine UTRACLOAD.

  1. Load ID (*DLOAD): VBF(E)
  2. FL−4T

  3. Viscous body force in global X-, Y-, and Z-directions.

  1. Load ID (*DLOAD): VP(E)
  2. FL−3T

  3. 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
  1. Load ID (*FOUNDATION): F(S)
  2. FL−3

  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
  1. Load ID (*DFLUX): BF(S)
  2. JL−3 T−1

  3. Body heat flux per unit volume.

  1. Load ID (*DFLUX): BFNU(S)
  2. JL−3 T−1

  3. Nonuniform body heat flux per unit volume with magnitude supplied via user subroutine DFLUX.

  1. Load ID (*DFLUX): MBFNU (S)
  2. JT−1

  3. Nonuniform moving or stationary concentrated heat fluxes with magnitudes supplied via user subroutine UMDFLUX.

  1. Load ID (*DFLUX): SNEG(S)
  2. JL−2 T−1

  3. Surface heat flux per unit area into the bottom face of the element.

  1. Load ID (*DFLUX): SPOS(S)
  2. JL−2 T−1

  3. Surface heat flux per unit area into the top face of the element.

  1. Load ID (*DFLUX): SNEGNU(S)
  2. JL−2 T−1

  3. Nonuniform surface heat flux per unit area into the bottom face of the element with magnitude supplied via user subroutine DFLUX.

  1. Load ID (*DFLUX): SPOSNU(S)
  2. JL−2 T−1

  3. 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
  1. Load ID (*FILM): FNEG(S)
  2. JL−2 T−1θ−1

  3. Film coefficient and sink temperature (units of θ) provided on the bottom face of the element.

  1. Load ID (*FILM): FPOS(S)
  2. JL−2 T−1θ−1

  3. Film coefficient and sink temperature (units of θ) provided on the top face of the element.

  1. Load ID (*FILM): FNEGNU(S)
  2. JL−2 T−1θ−1

  3. Nonuniform film coefficient and sink temperature (units of θ) provided on the bottom face of the element with magnitude supplied via user subroutine FILM.

  1. Load ID (*FILM): FPOSNU(S)
  2. JL−2 T−1θ−1

  3. Nonuniform film coefficient and sink temperature (units of θ) provided on the top face of the element with magnitude supplied via user subroutine FILM.

  1. Load ID (*FILM): FFS(S)
  2. JL−2 T−1θ−1

  3. Film coefficient and sink temperature (units of θ) provided on the top and bottom faces of the element.

  1. Load ID (*FILM): FFSNU(S)
  2. JL−2 T−1θ−1

  3. Nonuniform film coefficient and sink temperature (units of θ) provided on the top and bottom faces of the element with magnitude supplied via user subroutine.

Radiation Types

Radiation conditions are available for elements with temperature degrees of freedom. They are specified as described in Thermal Loads.

*radiate
  1. Load ID (*RADIATE): RNEG(S)
  2. Dimensionless

  3. Emissivity and sink temperature (units of θ) provided for the bottom face of the shell.

  1. Load ID (*RADIATE): RPOS(S)
  2. Dimensionless

  3. Emissivity and sink temperature (units of θ) provided for the top face of the shell.

  1. Load ID (*RADIATE): RFS(S)
  2. Dimensionless

  3. Emissivity and sink temperature (units of θ) provided for the top and bottom faces 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
  1. Load ID (*DSLOAD): EDLD
  2. FL−1

  3. General traction on edge-based surface.

  1. Load ID (*DSLOAD): EDLDNU(S)
  2. FL−1

  3. Nonuniform general traction on edge-based surface with magnitude and direction supplied via user subroutine UTRACLOAD.

  1. Load ID (*DSLOAD): EDMOM
  2. F

  3. Moment on edge-based surface.

  1. Load ID (*DSLOAD): EDMOMNU(S)
  2. F

  3. Nonuniform moment on edge-based surface with magnitude supplied via user subroutine UTRACLOAD.

  1. Load ID (*DSLOAD): EDNOR
  2. FL−1

  3. Normal traction on edge-based surface.

  1. Load ID (*DSLOAD): EDNORNU(S)
  2. FL−1

  3. Nonuniform normal traction on edge-based surface with magnitude supplied via user subroutine UTRACLOAD.

  1. Load ID (*DSLOAD): EDSHR
  2. FL−1

  3. Shear traction on edge-based surface.

  1. Load ID (*DSLOAD): EDSHRNU(S)
  2. FL−1

  3. Nonuniform shear traction on edge-based surface with magnitude supplied via user subroutine UTRACLOAD.

  1. Load ID (*DSLOAD): EDTRA
  2. FL−1

  3. Transverse traction on edge-based surface.

  1. Load ID (*DSLOAD): EDTRANU(S)
  2. FL−1

  3. Nonuniform transverse traction on edge-based surface with magnitude supplied via user subroutine UTRACLOAD.

  1. Load ID (*DSLOAD): HP(S)
  2. FL−2

  3. Hydrostatic pressure on the element reference surface and linear in global Z. The pressure is positive in the direction opposite to the surface normal.

  1. Load ID (*DSLOAD): P
  2. FL−2

  3. Pressure on the element reference surface. The pressure is positive in the direction opposite to the surface normal.

  1. Load ID (*DSLOAD): PNU
  2. FL−2

  3. 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.

  1. Load ID (*DSLOAD): SP(E)
  2. FL−4T2

  3. Stagnation pressure applied to the element reference surface.

  1. Load ID (*DSLOAD): TRSHR
  2. FL−2

  3. Shear traction on the element reference surface.

  1. Load ID (*DSLOAD): TRSHRNU(S)
  2. FL−2

  3. Nonuniform shear traction on the element reference surface with magnitude and direction supplied via user subroutine UTRACLOAD.

  1. Load ID (*DSLOAD): TRVEC
  2. FL−2

  3. General traction on the element reference surface.

  1. Load ID (*DSLOAD): TRVECNU(S)
  2. FL−2

  3. Nonuniform general traction on the element reference surface with magnitude and direction supplied via user subroutine UTRACLOAD.

  1. Load ID (*DSLOAD): VP(E)
  2. FL−3T

  3. 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
  1. Load ID (*DSFLUX): S(S)
  2. JL−2 T−1

  3. Surface heat flux per unit area into the element surface.

  1. Load ID (*DSFLUX): SNU(S)
  2. JL−2 T−1

  3. 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
  1. Load ID (*SFILM): F(S)
  2. JL−2 T−1θ−1

  3. Film coefficient and sink temperature (units of θ) provided on the element surface.

  1. Load ID (*SFILM): FNU(S)
  2. JL−2 T−1θ−1

  3. Nonuniform film coefficient and sink temperature (units of θ) 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
  1. Load ID (*SRADIATE): R(S)
  2. Dimensionless

  3. Emissivity and sink temperature (units of θ) provided for the element surface.

Incident Wave Loading

Surface-based incident wave loads are available. They are specified as described in Acoustic, Shock, and Coupled Acoustic-Structural Analysis. If the incident wave field includes a reflection off a plane outside the boundaries of the mesh, this effect can be included.

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 11 direct stress.

S22

Local 22 direct stress.

S12

Local 12 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

(S⁢F⁢1,S⁢F⁢2,S⁢F⁢3,S⁢F⁢4,S⁢F⁢5)​=∫-h/2-z0h/2-z0(σ11,σ22,σ12,σ13,σ23)⁢d⁢z,(S⁢M⁢1,S⁢M⁢2,S⁢M⁢3)​=∫-h/2-z0h/2-z0(σ11,σ22,σ12)⁢z⁢d⁢z,

where z0 is the offset of the reference surface from the midsurface.

The section force SF6, which is the integral of σ33 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

(S⁢S⁢A⁢V⁢G⁢1,S⁢S⁢A⁢V⁢G⁢2,S⁢S⁢A⁢V⁢G⁢3,S⁢S⁢A⁢V⁢G⁢4,S⁢S⁢A⁢V⁢G⁢5)​=(S⁢F⁢1,S⁢F⁢2,S⁢F⁢3,S⁢F⁢4,S⁢F⁢5)/h,

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 each layer of the shell section is defined using an elastic material model or a user-defined material model with the elastic transverse shear moduli defined. 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



 

Heat Transfer Analysis