SHELL61

Axisymmetric-Harmonic Structural Shell

SHELL61 Element Description

SHELL61 has four degrees of freedom at each node: translations in the nodal x, y, and z directions and a rotation about the nodal z-axis. The loading may be axisymmetric or nonaxisymmetric. Various loading cases are described in Harmonic Axisymmetric Elements with Nonaxisymmetric Loads.

Extreme orientations of the conical shell element result in a cylindrical shell element or an annular disc element. The shell element may have a linearly varying thickness. See SHELL61 in the Mechanical APDL Theory Reference for more details about this element.

Figure 61.1: SHELL61 Geometry

SHELL61 Input Data

The geometry, node locations, and the coordinate system for this element are shown in Figure 61.1: SHELL61 Geometry. The element is defined by two nodes, two end thicknesses, the number of harmonic waves (MODE on the MODE command), a symmetry condition (ISYM on the MODE command), and the orthotropic material properties. The element coordinate system is shown in Figure 61.2: SHELL61 Stress Output. θ is in the tangential (hoop) direction. The MODE or ISYM parameters are discussed in detail in Harmonic Axisymmetric Elements with Nonaxisymmetric Loads.

The material may be orthotropic, with nine elastic constants required for its description. The element loading may be input as any combination of harmonically varying temperatures and pressures. Harmonically varying nodal forces, if any, should be input on a full 360° basis.

The element may have variable thickness. The thickness is assumed to vary linearly between the nodes. If the element has a constant thickness, only TK(I) is required. Real constant ADMSUA is used to define an added mass per unit area.

Element loads are described in Element Loading. Harmonically varying pressures may be input as surface loads on the element faces as shown by the circled numbers on Figure 61.1: SHELL61 Geometry. Positive pressures act into the element. The pressures are applied at the surface of the element rather than at the centroidal plane so that some thickness effects can be considered. These include the increase or decrease in size of surface area the load is acting on and (in the case of a nonzero Poisson's ratio) an interaction effect causing the element to grow longer or shorter under equal pressures on both surfaces. Material properties EY, PRXY, and PRYZ (or EY, NUXY, and NUYZ) are required for this effect.

Harmonically varying temperatures may be input as element body loads at the four corner locations shown in Figure 61.1: SHELL61 Geometry. The first corner temperature T1 defaults to TUNIF. If all other temperatures are unspecified, they default to T1. If only T1 and T2 are input, T3 defaults to T2 and T4 defaults to T1. For any other input pattern, unspecified temperatures default to TUNIF.

KEYOPT(1) is used for temperature loading with MODE greater than zero and temperature-dependent material properties. Material properties may only be evaluated at a constant (nonharmonically varying) temperature. If MODE equals zero, the material properties are always evaluated at the average element temperature. KEYOPT(3) is used to include or suppress the extra displacement shapes.

A summary of the element input is given in "SHELL61 Input Summary". A general description of element input is given in Element Input.

SHELL61 Input Summary

Nodes

I, J

Degrees of Freedom

UX, UY, UZ, ROTZ

Real Constants

TK(I) - Shell thickness at node I

TK(J) - Shell thickness at node J (TK(J) defaults to TK(I))

ADMSUA - Added mass/unit area

Material Properties

MP command: EX, EY, EZ, PRXY, PRYZ, PRXZ (or NUXY, NUYZ, NUXZ), ALPX, ALPZ (or CTEX, CTEY, CTEZ or THSX, THSY, THSZ), DENS, GXZ, ALPD, BETD. (X is meridional, Y is through-the-thickness, and Z is circumferential), DMPR, DMPS

Surface Loads

Pressures --

face 1 (I-J) (top, in -Y direction)

face 2 (I-J) (bottom, in +Y direction)

Body Loads

Temperatures --: T1, T2, T3, T4

Mode Number

Number of harmonic waves around the circumference (MODE)

Loading Condition

Symmetry condition (MODE)

Special Features

Stress stiffening

KEYOPT(1)

If MODE is greater than zero, use temperatures for:

0 --: Use temperatures only for thermal bending (evaluate material properties at TREF)
1 --: Use temperatures only for material property evaluation (thermal strains are not computed)

KEYOPT(3)

Extra displacement shapes:

0 --: Include extra displacement shapes
1 --: Suppress extra displacement shapes

KEYOPT(4)

Member force and moment output:

0 --: No printout of member forces and moments
1 --: Print out member forces and moments in the element coordinate system

KEYOPT(6)

Location of element solution output:

0 --: Output solution at mid-length only
N --: Output solution at N equally spaced interior points and at end points (where N = 1, 3, 5, 7 or 9)

SHELL61 Output Data

The solution output associated with the element is in two forms:

Nodal displacements included in the overall nodal solution
Additional element output as shown in Table 61.1: SHELL61 Element Output Definitions

Several items are illustrated in Figure 61.2: SHELL61 Stress Output. The printout may be displayed at the centroid, at the end points and at N equally spaced interior points, where N is the KEYOPT(6) value. For example, if N = 3, printout will be produced at end I, 1/4 length, mid-length (centroid), 3/4 length, and at end J. Printout location number 1 is always at end I. Stress components which are inherently zero are printed for clarity.

In the displacement printout, the UZ components are out-of-phase with the UX and UY components. For example, in the MODE = 1, ISYM = 1 loading case, UX and UY are the peak values at θ = 0° and UZ is the peak value at θ = 90°. We recommend that you always use the angle field on the SET command when postprocessing the results. For more information about harmonic elements, see Harmonic Axisymmetric Elements with Nonaxisymmetric Loads

A general description of solution output is given in Solution Output. See the Basic Analysis Guide for ways to view results.

Figure 61.2: SHELL61 Stress Output

The Element Output Definitions table uses the following notation:

A colon (:) in the Name column indicates that the item can be accessed by the Component Name method (ETABLE, ESOL). The O column indicates the availability of the items in the file jobname.out. The R column indicates the availability of the items in the results file.

In either the O or R columns, “Y” indicates that the item is always available, a letter or number refers to a table footnote that describes when the item is conditionally available, and “-” indicates that the item is not available.

Table 61.1: SHELL61 Element Output Definitions

Name	Definition	O	R
EL	Element Number	Y	Y
NODES	Nodes - I, J	Y	Y
MAT	Material number	Y	Y
LENGTH	Distance between node I and node J	Y	Y
XC, YC	Location where results are reported	Y	2
TEMP	Temperatures T1, T2, T3, T4	Y	Y
PRES	Pressures P1 (top) at nodes I,J; P2 (bottom) at nodes I,J	Y	Y
MODE	Number of waves in loading	Y	Y
ISYM	Loading key: 1 = symmetric, -1 = antisymmetric	Y	Y
T(X, Z, XZ)	In-plane element X, Z, and XZ forces at KEYOPT(6) location(s)	Y	Y
M(X, Z, XZ)	Out-of-plane element X, Z, and XZ moments at KEYOPT(6) location(s)	Y	Y
MFOR(X, Y, Z), MMOMZ	Member forces and member moment for each node in the element coordinate system	1	Y
PK ANG	Angle where stresses have peak values: 0 and 90/MODE°. Blank if `MODE` = 0.	Y	Y
S(M, THK, H, MH)	Stresses (meridional, through-thickness, hoop, meridional-hoop) at PK ANG locations, repeated for top, middle, and bottom of shell	Y	Y
EPEL(M, THK, H, MH)	Elastic strains (meridional, through-thickness, hoop, meridional-hoop) at PK ANG locations, repeated for top, middle, and bottom of shell	Y	Y
EPTH(M, THK, H, MH)	Thermal strains (meridional, through-thickness, hoop, meridional-hoop) at PK ANG locations, repeated for top, middle, and bottom of shell	Y	Y

These items are printed only if KEYOPT(4) = 1.
Available only at centroid as a *GET item.

Table 61.2: SHELL61 Item and Sequence Numbers (KEYOPT(6) = 0 or 1) lists output available through the ETABLE command using the Sequence Number method. See The General Postprocessor (POST1) in the Basic Analysis Guide and The Item and Sequence Number Table in this reference for more information. The following notation is used in Table 61.2: SHELL61 Item and Sequence Numbers (KEYOPT(6) = 0 or 1):

Name: output quantity as defined in the Table 61.1: SHELL61 Element Output Definitions
Item: predetermined Item label for ETABLE command
I,J: sequence number for data at nodes I and J
ILn: sequence number for data at Intermediate Location n

Table 61.2: SHELL61 Item and Sequence Numbers (KEYOPT(6) = 0 or 1)

Output Quantity Name	ETABLE and ESOL Command Input
Output Quantity Name	Item	I	IL1	J
Top
SM	LS	1	13	25
STHK	LS	2	14	26
SH	LS	3	15	27
SMH	LS	4	16	28
EPELM	LEPEL	1	13	25
EPELTHK	LEPEL	2	14	26
EPELH	LEPEL	3	15	27
EPELMH	LEPEL	4	16	28
EPTHM	LEPTH	1	13	25
EPTHTHK	LEPTH	2	14	26
EPTHH	LEPTH	3	15	27
EPTHMH	LEPTH	4	16	28
Mid
SM	LS	5	17	29
STHK	LS	6	18	30
SH	LS	7	19	31
SMH	LS	8	20	32
EPELM	LEPEL	5	17	29
EPELTHK	LEPEL	6	18	30
EPELH	LEPEL	7	19	31
EPELMH	LEPEL	8	20	32
EPTHM	LEPTH	5	17	29
EPTHTHK	LEPTH	6	18	30
EPTHH	LEPTH	7	19	31
EPTHMH	LEPTH	8	20	32
Bot
SM	LS	9	21	33
STHK	LS	10	22	34
SH	LS	11	23	35
SMH	LS	12	24	36
EPELM	LEPEL	9	21	33
EPELTHK	LEPEL	10	22	34
EPELH	LEPEL	11	23	35
EPELMH	LEPEL	12	24	36
EPTHM	LEPTH	9	21	33
EPTHTHK	LEPTH	10	22	34
EPTHH	LEPTH	11	23	35
EPTHMH	LEPTH	12	24	36
Element
MFORX	SMISC	1	-	7
MFORY	SMISC	2	-	8
MFORZ	SMISC	3	-	9
MMOMZ	SMISC	6	-	12
TX	SMISC	13	19	25
TZ	SMISC	14	20	26
TXZ	SMISC	15	21	27
MX	SMISC	16	22	28
MZ	SMISC	17	23	29
MXZ	SMISC	18	24	30
P1	SMISC	31	-	32
P2	SMISC	35	-	36

		Corner Location
		1	2	3	4
TEMP	LBFE	1	2	3	4

Table 61.3: SHELL61 Item and Sequence Numbers (KEYOPT(6) = 3)

Output Quantity Name	ETABLE and ESOL Command Input
Output Quantity Name	Item	I	IL1	IL2	IL3	J
Top
SM	LS	1	13	25	37	49
STHK	LS	2	14	26	38	50
SH	LS	3	15	27	39	51
SMH	LS	4	16	28	40	52
EPELM	LEPEL	1	13	25	37	49
EPELTHK	LEPEL	2	14	26	38	50
EPELH	LEPEL	3	15	27	39	51
EPELMH	LEPEL	4	16	28	40	52
EPTHM	LEPTH	1	13	25	37	49
EPTHTHK	LEPTH	2	14	26	38	50
EPTHH	LEPTH	3	15	27	39	51
EPTHMH	LEPTH	4	16	28	40	52
Mid
SM	LS	5	17	29	41	53
STHK	LS	6	18	30	42	54
SH	LS	7	19	31	43	55
SMH	LS	8	20	32	44	56
EPELM	LEPEL	5	17	29	41	53
EPELTHK	LEPEL	6	18	30	42	54
EPELH	LEPEL	7	19	31	43	55
EPELMH	LEPEL	8	20	32	44	56
EPTHM	LEPTH	5	17	29	41	53
EPTHTHK	LEPTH	6	18	30	42	54
EPTHH	LEPTH	7	19	31	43	55
EPTHMH	LEPTH	8	20	32	44	56
Bot
SM	LS	9	21	33	45	57
STHK	LS	10	22	34	46	58
SH	LS	11	23	35	47	59
SMH	LS	12	24	36	48	60
EPELM	LEPEL	9	21	33	45	57
EPELTHK	LEPEL	10	22	34	46	58
EPELH	LEPEL	11	23	35	47	59
EPELMH	LEPEL	12	24	36	48	60
EPTHM	LEPTH	9	21	33	45	57
EPTHTHK	LEPTH	10	22	34	46	58
EPTHH	LEPTH	11	23	35	47	59
EPTHMH	LEPTH	12	24	36	48	60
Element
MFORX	SMISC	1	-	-	-	7
MFORY	SMISC	2	-	-	-	8
MFORZ	SMISC	3	-	-	-	9
MMOMZ	SMISC	6	-	-	-	12
TX	SMISC	13	19	25	31	37
TZ	SMISC	14	20	26	32	38
TXZ	SMISC	15	21	27	33	39
MX	SMISC	16	22	28	34	40
MZ	SMISC	17	23	29	35	41
MXZ	SMISC	18	24	30	36	42
P1	SMISC	43	-	-	-	44
P2	SMISC	47	-	-	-	48

		Corner Location
		1	2	3	4
TEMP	LBFE	1	2	3	4

Table 61.4: SHELL61 Item and Sequence Numbers (KEYOPT(6) = 5)

Output Quantity Name	ETABLE and ESOL Command Input
Output Quantity Name	Item	I	IL1	IL2	IL3	IL4	IL5	J
Top
SM	LS	1	13	25	37	49	61	73
STHK	LS	2	14	26	38	50	62	74
SH	LS	3	15	27	39	51	63	75
SMH	LS	4	16	28	40	52	64	76
EPELM	LEPEL	1	13	25	37	49	61	73
EPELTHK	LEPEL	2	14	26	38	50	62	74
EPELH	LEPEL	3	15	27	39	51	63	75
EPELMH	LEPEL	4	16	28	40	52	64	76
EPTHM	LEPTH	1	13	25	37	49	61	73
EPTHTHK	LEPTH	2	14	26	38	50	62	74
EPTHH	LEPTH	3	15	27	39	51	63	75
EPTHMH	LEPTH	4	16	28	40	52	64	76
Mid
SM	LS	5	17	29	41	53	65	77
STHK	LS	6	18	30	42	54	66	78
SH	LS	7	19	31	43	55	67	79
SMH	LS	8	20	32	44	56	68	80
EPELM	LEPEL	5	17	29	41	53	65	77
EPELTHK	LEPEL	6	18	30	42	54	66	78
EPELH	LEPEL	7	19	31	43	55	67	79
EPELMH	LEPEL	8	20	32	44	56	68	80
EPTHM	LEPTH	5	17	29	41	53	65	77
EPTHTHK	LEPTH	6	18	30	42	54	66	78
EPTHH	LEPTH	7	19	31	43	55	67	79
EPTHMH	LEPTH	8	20	32	44	56	68	80
Bot
SM	LS	9	21	33	45	57	69	81
STHK	LS	10	22	34	46	58	70	82
SH	LS	11	23	35	47	59	71	83
SMH	LS	12	24	36	48	60	72	84
EPELM	LEPEL	9	21	33	45	57	69	81
EPELTHK	LEPEL	10	22	34	46	58	70	82
EPELH	LEPEL	11	23	35	47	59	71	83
EPELMH	LEPEL	12	24	36	48	60	72	84
EPTHM	LEPTH	9	21	33	45	57	69	81
EPTHTHK	LEPTH	10	22	34	46	58	70	82
EPTHH	LEPTH	11	23	35	47	59	71	83
EPTHMH	LEPTH	12	24	36	48	60	72	84
Element
MFORX	SMISC	1	-	-	-	-	-	7
MFORY	SMISC	2	-	-	-	-	-	8
MFORZ	SMISC	3	-	-	-	-	-	9
MMOMZ	SMISC	6	-	-	-	-	-	12
TX	SMISC	13	19	25	31	37	43	49
TZ	SMISC	14	20	26	32	38	44	50
TXZ	SMISC	15	21	27	33	39	45	51
MX	SMISC	16	22	28	34	40	46	52
MZ	SMISC	17	23	29	35	41	47	53
MXZ	SMISC	18	24	30	36	42	48	54
P1	SMISC	55	-	-	-	-	-	56
P2	SMISC	59	-	-	-	-	-	60

		Corner Location
		1	2	3	4
TEMP	LBFE	1	2	3	4

Table 61.5: SHELL61 Item and Sequence Numbers (KEYOPT(6) = 7)

Output Quantity Name	ETABLE and ESOL Command Input
Output Quantity Name	Item	I	IL1	IL2	IL3	IL4	IL5	IL6	IL7	J
Top
SM	LS	1	13	25	37	49	61	73	85	97
STHK	LS	2	14	26	38	50	62	74	86	98
SH	LS	3	15	27	39	51	63	75	87	99
SMH	LS	4	16	28	40	52	64	76	88	100
EPELM	LEPEL	1	13	25	37	49	61	73	85	97
EPELTHK	LEPEL	2	14	26	38	50	62	74	86	98
EPELH	LEPEL	3	15	27	39	51	63	75	87	99
EPELMH	LEPEL	4	16	28	40	52	64	76	88	100
EPTHM	LEPTH	1	13	25	37	49	61	73	85	97
EPTHTHK	LEPTH	2	14	26	38	50	62	74	86	98
EPTHH	LEPTH	3	15	27	39	51	63	75	87	99
EPTHMH	LEPTH	4	16	28	40	52	64	76	88	100
Mid
SM	LS	5	17	29	41	53	65	77	89	101
STHK	LS	6	18	30	42	54	66	78	90	102
SH	LS	7	19	31	43	55	67	79	91	103
SMH	LS	8	20	32	44	56	68	80	92	104
EPELM	LEPEL	5	17	29	41	53	65	77	89	101
EPELTHK	LEPEL	6	18	30	42	54	66	78	90	102
EPELH	LEPEL	7	19	31	43	55	67	79	91	103
EPELMH	LEPEL	8	20	32	44	56	68	80	92	104
EPTHM	LEPTH	5	17	29	41	53	65	77	89	101
EPTHTHK	LEPTH	6	18	30	42	54	66	78	90	102
EPTHH	LEPTH	7	19	31	43	55	67	79	91	103
EPTHMH	LEPTH	8	20	32	44	56	68	80	92	104
Bot
SM	LS	9	21	33	45	57	69	81	93	105
STHK	LS	10	22	34	46	58	70	82	94	106
SH	LS	11	23	35	47	59	71	83	95	107
SMH	LS	12	24	36	48	60	72	84	96	108
EPELM	LEPEL	9	21	33	45	57	69	81	93	105
EPELTHK	LEPEL	10	22	34	46	58	70	82	94	106
EPELH	LEPEL	11	23	35	47	59	71	83	95	107
EPELMH	LEPEL	12	24	36	48	60	72	84	96	108
EPTHM	LEPTH	9	21	33	45	57	69	81	93	105
EPTHTHK	LEPTH	10	22	34	46	58	70	82	94	106
EPTHH	LEPTH	11	23	35	47	59	71	83	95	107
EPTHMH	LEPTH	12	24	36	48	60	72	84	96	108
Element
MFORX	SMISC	1	-	-	-	-	-	-	-	7
MFORY	SMISC	2	-	-	-	-	-	-	-	8
MFORZ	SMISC	3	-	-	-	-	-	-	-	9
MMOMZ	SMISC	6	-	-	-	-	-	-	-	12
TX	SMISC	13	19	25	31	37	43	49	55	61
TZ	SMISC	14	20	26	32	38	44	50	56	62
TXZ	SMISC	15	21	27	33	39	45	51	57	63
MX	SMISC	16	22	28	34	40	46	52	58	64
MZ	SMISC	17	23	29	35	41	47	53	59	65
MXZ	SMISC	18	24	30	36	42	48	54	60	66
P1	SMISC	67	-	-	-	-	-	-	-	68
P2	SMISC	71	-	-	-	-	-	-	-	72

		Corner Location
		1	2	3	4
TEMP	LBFE	1	2	3	4

Table 61.6: SHELL61 Item and Sequence Numbers (KEYOPT(6) = 9)

Output Quantity Label	ETABLE and ESOL Command Input
Output Quantity Label	Item	I	IL1	IL2	IL3	IL4	IL5	IL6	IL7	IL8	IL9	J
Top
SM	LS	1	13	25	37	49	61	73	85	97	109	121
STHK	LS	2	14	26	38	50	62	74	86	98	110	122
SH	LS	3	15	27	39	51	63	75	87	99	111	123
SMH	LS	4	16	28	40	52	64	76	88	100	112	124
EPELM	LEPEL	1	13	25	37	49	61	73	85	97	109	121
EPELTHK	LEPEL	2	14	26	38	50	62	74	86	98	110	122
EPELH	LEPEL	3	15	27	39	51	63	75	87	99	111	123
EPELMH	LEPEL	4	16	28	40	52	64	76	88	100	112	124
EPTHM	LEPTH	1	13	25	37	49	61	73	85	97	109	121
EPTHTHK	LEPTH	2	14	26	38	50	62	74	86	98	110	122
EPTHH	LEPTH	3	15	27	39	51	63	75	87	99	111	123
EPTHMH	LEPTH	4	16	28	40	52	64	76	88	100	112	124
Mid
SM	LS	5	17	29	41	53	65	77	89	101	113	125
STHK	LS	6	18	30	42	54	66	78	90	102	114	126
SH	LS	7	19	31	43	55	67	79	91	103	115	127
SMH	LS	8	20	32	44	56	68	80	92	104	116	128
EPELM	LEPEL	5	17	29	41	53	65	77	89	101	113	125
EPELTHK	LEPEL	6	18	30	42	54	66	78	90	102	114	126
EPELH	LEPEL	7	19	31	43	55	67	79	91	103	115	127
EPELMH	LEPEL	8	20	32	44	56	68	80	92	104	116	128
EPTHM	LEPTH	5	17	29	41	53	65	77	89	101	113	125
EPTHTHK	LEPTH	6	18	30	42	54	66	78	90	102	114	126
EPTHH	LEPTH	7	19	31	43	55	67	79	91	103	115	127
EPTHMH	LEPTH	8	20	32	44	56	68	80	92	104	116	128
Bot
SM	LS	9	21	33	45	57	69	81	93	105	117	129
STHK	LS	10	22	34	46	58	70	82	94	106	118	130
SH	LS	11	23	35	47	59	71	83	95	107	119	131
SMH	LS	12	24	36	48	60	72	84	96	108	120	132
EPELM	LEPEL	9	21	33	45	57	69	81	93	105	117	129
EPELTHK	LEPEL	10	22	34	46	58	70	82	94	106	118	130
EPELH	LEPEL	11	23	35	47	59	71	83	95	107	119	131
EPELMH	LEPEL	12	24	36	48	60	72	84	96	108	120	132
EPTHM	LEPTH	9	21	33	45	57	69	81	93	105	117	129
EPTHTHK	LEPTH	10	22	34	46	58	70	82	94	106	118	130
EPTHH	LEPTH	11	23	35	47	59	71	83	95	107	119	131
EPTHMH	LEPTH	12	24	36	48	60	72	84	96	108	120	132
Element
MFORX	SMISC	1	-	-	-	-	-	-	-	-	-	7
MFORY	SMISC	2	-	-	-	-	-	-	-	-	-	8
MFORZ	SMISC	3	-	-	-	-	-	-	-	-	-	9
MMOMZ	SMISC	6	-	-	-	-	-	-	-	-	-	12
TX	SMISC	13	19	25	31	37	43	49	55	61	67	73
TZ	SMISC	14	20	26	32	38	44	50	56	62	68	74
TXZ	SMISC	15	21	27	33	39	45	51	57	63	69	75
MX	SMISC	16	22	28	34	40	46	52	58	64	70	76
MZ	SMISC	17	23	29	35	41	47	53	59	65	71	77
MXZ	SMISC	18	24	30	36	42	48	54	60	66	72	78
P1	SMISC	79	-	-	-	-	-	-	-	-	-	80
P2	SMISC	83	-	-	-	-	-	-	-	-	-	84

		Corner Location
		1	2	3	4
TEMP	LBFE	1	2	3	4

SHELL61 Assumptions and Restrictions

The axisymmetric shell element must be defined in the global X-Y plane and must not have a zero length. Both ends must have nonnegative X coordinate values and the element must not lie along the global Y-axis.
If the element has a constant thickness, only TK(I) need be defined. TK(I) must not be zero.
The element thickness is assumed to vary linearly from node I to node J.
The element assumes a linear elastic material.
Post analysis superposition of results is valid only with other linear elastic solutions.
Strain energy does not consider thermal effects.
The element should not be used with the large deflection option.
The element may not be deactivated with the EKILL command.
You can use only axisymmetric (MODE,0) loads without significant torsional stresses to generate the stress state used for stress stiffened modal analyses using this element.

SHELL61 Product Restrictions

There are no product-specific restrictions for this element.