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Finite Element Analysis in Structural Mechanics

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en:ref:name:i2

Table of Contents

name.i2

Program

RPD2 RPD3

Format

; program control IP KREST

; optional description of independent variables IV JIV T IV V $x_1$ $x_2$ $\dots$ $x_N$

; material quantities MP ISET T 1 V $E$ $\alpha$ $\nu$ $\rho$ $\sigma_Y$ $Q_Y$ ${\dot\varepsilon}_c$ $\Phi$

; nodal displacements for the whole mesh GV ISET T 1 V $[u]_1$ $\dots$ $[u]_\mathtt{NNOD}$ GV ISET T 1 D 12 IREC

; nodal temperatures for the whole mesh GV ISET T 6 V $[T]_1$ $\dots$ $[T]_\mathtt{NNOD}$ GV ISET T 6 D 4 IREC

; volumetric loading VV ISET T 6 V $Q_x$ $Q_y$ $Q_z$

; Winkler’s foundation SV ISET T 2 V $K_n$ $K_t$ ; in the local coordinate system of an isoparametric element’s face SV ISET T 2 V $K_\xi$ $K_\eta$ $K_\zeta$ ; in the local coordinate system of a semi-loof element’ face SV ISET T 3 V $K_x$ $K_y$ $K_z$ ; in the global coordinate system

; surface loading SV ISET T 6 V $q_n$ ; in the direction of the element’s face normal SV ISET T 9 V $q_x$ $q_y$ $q_z$ ; in the global coordinate system

; contact surfaces (see notes below) SV ISET T 10 V 0 ; surface A SV ISET T 11 V 0 ; surface B

; spring edge support LV ISET T 2 V $K_{x_h}$ $K_{y_h}$ $K_{z_h}$ $C_{y_h}$ ; in the local coordinate system of the semi-loof element’s edge

; line loading LV ISET T 6 V $l_{x_h}$ $l_{y_h}$ $l_{z_h}$ $m_{y_h}$ ; in the local coordinate system of the semi-loof element’s edge LV ISET T 9 V $l_x$ $l_y$ $l_z$ ; in the global coordinate system

; nodal displacement NV ISET T 1 V $u$ $v$ $w$ ; 3 components NV ISET T 1 V $u$ $v$ $w$ $\alpha$ $\beta$ ; 5 components NV ISET T 1 V $u$ $v$ $w$ $\varphi_x$ $\varphi_y$ $\varphi_z$ ; 6 components NV ISET T 1 C $[$IC$]$ V $[u]$ ; only selected components

; spring NV ISET T 2 N IN V $k_n$ $k_t$ $\cos(n,x)$ $\cos(n,y)$ $\cos(n,z)$ ; in a general direction NV ISET T 3 N IN V $k_x$ $k_y$ $k_z$ ; in the global coordinate system NV ISET T 4 N IN V $k_{11}$ $k_{12}$ $k_{22}$ $k_{13}$ $k_{23}$ $k_{33}$ $\dots$ $k_{1m}$ $k_{2m}$ $\dots$ $k_{mm}$ ; symmetric stiffness matrix in the global coordinate system

; nodal force NV ISET T 6 V $F_x$ $F_y$ $F_z$ ; 3 components NV ISET T 6 V $F_x$ $F_y$ $F_z$ $M_\alpha$ $M_\beta$ ; 5 components NV ISET T 6 V $F_x$ $F_y$ $F_z$ $M_x$ $M_y$ $M_z$ ; 6 components

; first load case (see notes below) AS 1

; assign MP sets ␣␣/M ISET ; mandatory default material assign to all elements ␣␣/M ISET E $[$IE$]$

; prescribe zero displacements ␣␣/B 0 N $[$IN$]$ ; for all components ␣␣/B 0 C $[$IC$]$ N $[$IN$]$ ; only for selected components

; assign GV sets ␣␣/G ISET

; assign VV sets ␣␣/V ISET E $[$IE$]$

; assign SV sets ␣␣/S ISET E $[$IE$]$ S IS

; assign LV sets ␣␣/L ISET E $[$IE$]$ L IH

; assign NV sets ␣␣/N ISET N $[$IN$]$ ␣␣/N ISET E $[$IE$]$ ; only for nodal spring assigns

; prescribe constants ␣␣/R $R_m$ $T_o$ $T_w$ $\varepsilon_{z0}$

; optional other load cases (see notes below) AS 2 /$\dots$ /$\dots$ $\vdots$

; end of input data EN EN

All quantities may be assigned in the first load case. Quantities with $\mathtt{KQT}\le5$ are valid for all load cases. In the second and other load cases, only quantities with $\mathtt{KQT}>5$ may be assigned. Those quantities are valid only for the particular load case.

Contact pairs (there may be many) are entered by even first (surface A) and odd second (surface B) value of $\mathtt{KQT}$ (e.g., 10 and 11, 12 and 13, 102 and 103). Outside normals of the contact pair surfaces must be oriented oppositely!

Annotations

$\mathtt{KREST}$The key of restart.
$=1$start a new computation
$=2$process only additional load cases
$\cos(n,x)$ $\cos(n,y)$ $\cos(n,z)$The directional cosines of the spring axis.
$C_{y_h}$The moment stiffness of the edge support of the semi-loof element $[\text{Nm}/\text{rad}\!\cdot\!\text{m}].$
$E$The modulus of elasticity $[\text{Pa}].$
$F_x,F_y,F_z$The nodal force components in the direction of global axes.
$[\mathtt{IC}]$The list of local nodal generalized displacement components. Possible values are: $1\equiv u,$ $2\equiv v,$ $3\equiv w,$ $4\equiv\alpha\equiv\varphi_x,$ $5\equiv\beta\equiv\varphi_y$ a $6\equiv\varphi_z.$
$[\mathtt{IE}]$The list of element numbers.
$\mathtt{IH}$The local number of the element’s edge.
$\mathtt{IN}$The number of the node.
$[\mathtt{IN}]$The list of node numbers.
$\mathtt{IREC}$The number of the record in the binary file name.SOL (displacement field) or name.TEM (temperature field).
$\mathtt{IS}$The local number of the element’s face.
$\mathtt{ISET}$The identification number of the data set.
$\mathtt{IV}$The identification number of the variable.
$\mathtt{JIV}$The number of the IV batch.
$k_{11},\dots,k_{mm}$The entries of the symmetric stiffness matrix of the spring (upper triangle linearized column-wise). The number of entries must be equal to $m(m+1)/2,$ where $m$ is the number of degrees of freedom in the node in which the spring is connected.
$k_n,k_t$The normal and transverse stiffnesses of the spring $[\text{N}/\text{m}].$
$K_n,K_t$The normal and tangential stiffnesses of the Winkler foundation $[\text{Pa}/\text{m}].$
$\mathtt{KQT}$The identification number of the quantity.
$k_x,k_y,k_z$The stiffnesses of the spring in the global axes $[\text{N}/\text{m}].$
$K_x,K_y,K_z$The stiffnesses of the Winkler foundation in the direction of global axes $[\text{Pa}/\text{m}].$
$K_{x_h},K_{y_h},K_{z_h}$The stiffnesses of the edge reinforcement of the semi-loof element in the direction of local axes of the edge $[\text{N}/\text{m}^2].$
$K_\xi,K_\eta,K_\zeta$The stiffnesses of the Winkler foundation in the direction of local axes of the semi-loof element $[\text{Pa}/\text{m}].$
$l_x,l_y,l_z$The edge loading in the direction of global axes $[\text{N}/\text{m}].$
$l_{x_h},l_{y_h},l_{z_h}$The edge loading on the semi-loof element in the direction of local axes of the edge $[\text{N}/\text{m}].$
$M_x,M_y,M_z$The components of the moment in the direction of global axes in the node of the beam element $[\text{Nm}].$
$m_{y_h}$The edge moment on the semi-loof element in the direction of local axis of the edge $y_h$ $[\text{Nm}/\text{m}].$
$M_\alpha,M_\beta$The components of the moment on the edge of the semi-loof element $[\text{Nm}].$
$q_n$The surface loading in the normal direction to the element’s face $[\text{Pa}].$ Pressure is entered as a negative number.
$q_x,q_y,q_z$The components of the surface loading in the direction of global axes $[\text{Pa}].$
$Q_x,Q_y,Q_z$The components of the volumetric force in the direction of global axes $[\text{N}/\text{m}^3].$
$Q_Y$The kinematic hardening component $[\text{Pa}].$
$R_m$The number of revolutions $[1/\text{min}].$ The axis of rotation is $z.$
$[T]_1,\dots,[T]_\mathtt{NNOD}$The global temperature field. The number of components (the length of the vector) must be equal to the number of thermal degrees of freedom of the mesh exactly. If there are only 1-DOF nodes in the mesh the number of thermal degrees of freedom is identical to the number of mesh nodes.
$T_o$The initial (environment) temperature $[^\circ\text{C}].$
$T_w$The final (work) temperature $[^\circ\text{C}].$
$u,v,w$The nodal displacement in the direction of global axes $[\text{m}].$
$[u]$The prescribed components of the generalized nodal displacement. The order of values must follow the order of component numbers in the corresponding list $[\mathtt{IC}].$
$[u]_1,\dots,[u]_\mathtt{NNOD}$The global displacement field. The number of components (the length of the vector) must be equal to the number of degrees of freedom of the mesh exactly. If there are only nodes with translational DOFs in the mesh the number of degrees of freedom is equal to the number of mesh nodes times the problem dimension.
$x_1,\dots,x_N$The discrete values of the independent variable.
$\alpha$The integral coefficient of thermal expansion $[1/\text{K}].$
$\alpha,\beta$The angles of rotation of the edge of the semi-loof element $[\text{rad}].$
${\dot\varepsilon}_c$The rate of the effective creep strain $[1/\text{h}].$
$\varepsilon_{z0}$The nonzero plane strain $[1].$
$\nu$The Poisson number $[1].$
$\rho$The density $[\text{kg}/\text{m}^3].$
$\sigma_Y$The yield strength $[\text{Pa}].$
$\varphi_x,\varphi_y,\varphi_z$The angles of rotation of the edge of the beam element along the global axes $[\text{rad}].$
$\Phi$The dilation factor $[1].$
en/ref/name/i2.txt · Last modified: 2024-11-11 14:12 by Petr Pařík