elements:plxls
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elements:plxls [2019/03/14 16:56] helene |
elements:plxls [2020/08/25 15:46] (current) |
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| Plane state or axisymmetrical element \\ | Plane state or axisymmetrical element \\ | ||
| For the axisymmetrical element, the axis of symmetry must be the Y axis. \\ | For the axisymmetrical element, the axis of symmetry must be the Y axis. \\ | ||
| - | The element is defined by 3, 4, 6, or 8 nodes (see Input file) | + | The element is defined by 3, 4, 6, or 8 nodes (see Input file).\\ |
| + | For the generalised plane state, 8 nodes of the plane must be defined; the ninth is automatically the last one of the NODES section. \\ | ||
| + | |||
| + | The 4 nodes elements are not of very good quality: | ||
| + | * With 1 integration point, hourglass modes may appear | ||
| + | * With 4 integration points, locking (shear or volumetric) can occur. | ||
| + | {{ :elements:plxls.png?350|}} | ||
| Element type: 9 \\ | Element type: 9 \\ | ||
| - | Implemented by: ??? | + | Implemented by: J.P. Radu & J.D. Barnichon (1996) |
| - | {{ :elements:plxls.png?300|}} | ||
| ==== Files ==== | ==== Files ==== | ||
| - | Prepro: XXX.F \\ | + | Prepro: PLXLSA.F \\ |
| Lagamine: PLXLSB.F | Lagamine: PLXLSB.F | ||
| ===== Input file ===== | ===== Input file ===== | ||
| - | ^ TITLE (A5)^^ | + | ==== 1 - Title ==== |
| + | ^(A5)^^ | ||
| |TITLE|"PLXLS" in columns 1 to 5| | |TITLE|"PLXLS" in columns 1 to 5| | ||
| - | ^ Control (3I5) ^^ | + | |
| + | ==== 2 - Control ==== | ||
| + | ^ (3I5) ^^ | ||
| |NELEM| Number of elements | | |NELEM| Number of elements | | ||
| |ISPMAS|0 = nothing| | |ISPMAS|0 = nothing| | ||
| Line 26: | Line 35: | ||
| |INSIG| 0 if no initial stresses| | |INSIG| 0 if no initial stresses| | ||
| |:::| 1 or 2 if initial stresses| | |:::| 1 or 2 if initial stresses| | ||
| - | ^ Density (for dynamic analysis) (1G10.0) \\ Only if ISPMAS = 1^^ | + | |:::| 3 or 4 if residual stresses in cylinder| |
| + | |||
| + | ==== 3 - Density (dynamic analysis) ==== | ||
| + | __Only if ISPMAS = 1__ | ||
| + | ^(1G10.0)^^ | ||
| |SPEMAS|Density| | |SPEMAS|Density| | ||
| - | ^ Initial stresses (4G10.0) ^^ | + | |
| - | |If INSIG=1: $\sigma_y=\sigma_{y0}+yd\sigma_{y}$ \\ If INSIG=2: $\sigma_y=min(\sigma_{y0}+yd\sigma_y,0)$|| | + | ==== 4 - Initial stresses ==== |
| + | __Only if INSIG > 0__ | ||
| + | === Case 1: INSIG = 1 or 2 === | ||
| + | |||
| + | If INSIG=1: $\sigma_y=\sigma_{y0}+yd\sigma_{y}$ \\ If INSIG=2: $\sigma_y=min(\sigma_{y0}+yd\sigma_y,0)$ | ||
| + | ^ (4G10.0)^^ | ||
| |SIGY0| $\sigma_{y0}$ effective stress $\sigma_y$ at the axes origin| | |SIGY0| $\sigma_{y0}$ effective stress $\sigma_y$ at the axes origin| | ||
| |DSIGY|Effective stress gradient along Y axis| | |DSIGY|Effective stress gradient along Y axis| | ||
| |AK0X|$k_0$ ratio $\sigma_x/\sigma_y$| | |AK0X|$k_0$ ratio $\sigma_x/\sigma_y$| | ||
| |AK0Z|$k_0$ ratio $\sigma_z/\sigma_y$ (if AK0Z=0, AK0Z=AK0X)| | |AK0Z|$k_0$ ratio $\sigma_z/\sigma_y$ (if AK0Z=0, AK0Z=AK0X)| | ||
| - | ===== Results ===== | ||
| + | === Case 2: INSIG = 3 or 4 === | ||
| + | Generally, the radial stress $\sigma_r$ is assumed to be equal to zero. \\ | ||
| + | The longitudinal and circumferencial stresses, $\sigma_L$ & $\sigma_T$, are the same and given, for instance, by the following graph as a function of the depth/radius ratio: \\ | ||
| + | {{ :elements:plxls_resstress.png |}} | ||
| + | ^(6G10.0)^^ | ||
| + | |XC|X coordinate of the axis| | ||
| + | |YC|Y coordinate of the axis| | ||
| + | |R1 |radius of the cylinder| | ||
| + | |R2|radius corresponding to the maximum of tensile stress (point 2)| | ||
| + | |SIGC|maximum compression (observed on the external face of the cylinder) \\ :!: must be NEGATIVE| | ||
| + | |SIGT |maximum tensile stress (point 2)| | ||
| + | The following values are computed automatically: | ||
| + | |R3| radius corresponding to the point 3 \\ = R2 – ( R1 – R2 )| | ||
| + | |SIGR3 | stress corresponding to the point 3 \\ = ½ ( SIGT + SIGC )| | ||
| + | The stress on the axis is equal to zero. \\ | ||
| + | At each integration point, the initial stress SIGRES is computed according to the radius from this integration point to the center of the cylinder. \\ | ||
| + | In plane strain state (IANA=2) and generalised plane strain state (IANA=5), the stresses are the following ones: \\ | ||
| + | * SIGMA(1,IPI) = $\sigma_x = \sigma_1 . cos² \alpha + \sigma_2 . sin² \alpha$ \\ | ||
| + | * SIGMA(2,IPI) = $\sigma_y = \sigma_1 . sin² \alpha + \sigma_2 . cos² \alpha$ \\ | ||
| + | * SIGMA(3,IPI) = $\tau = ½ (\sigma_2-\sigma_1) . sin 2\alpha$ \\ | ||
| + | * SIGMA(4,IPI) = $\sigma_L$ = SIGRES \\ | ||
| + | |||
| + | where $\alpha$ is the angle between $\vec{r}$ and axis X and $\sigma_1$ & $\sigma_2$ the principal stresses in the plane (r,θ). In this case, $\sigma_1 = \sigma_{circ}$ = SIGRES and $\sigma_2 = \sigma_{rad}$ = ZERO. \\ | ||
| + | In axisymmetric state (IANA=3): | ||
| + | * SIGMA(1,IPI) = $\sigma_r$ = ZERO | ||
| + | * SIGMA(2,IPI) = $\sigma_T$ = SIGRES | ||
| + | * SIGMA(3,IPI) = $\tau$ = ZERO | ||
| + | * SIGMA(4,IPI) = $\sigma_L$ = SIGRES | ||
| + | |||
| + | ==== 5 - Definition of the elements ==== | ||
| + | |||
| + | ^ (3I5/8I5) ^^ | ||
| + | |NNODE| Number of nodes: 3, 4, 6, or 8| | ||
| + | |NINTE| Number of integration points: 1, 3, 4, 7, or 9| | ||
| + | |LMATE| Material | | ||
| + | |NODES(NNODE)| List of nodes| | ||
| + | |||
| + | ===== Results ===== | ||
| + | The mechanical Cauchy stresses are ordered as: $\sigma_x, \sigma_y, \tau_{xy}, \sigma_z$. These stresses are expressed in the global axis system. | ||
| + | |||
elements/plxls.1552578978.txt.gz · Last modified: 2020/08/25 15:34 (external edit)
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