2D Elements =========== 2D Elements ----------- .. _Tr1ht: Tr1ht element ~~~~~~~~~~~~~ Implements the linear triangular finite element for heat transfer problems. Each node has 1 degree of freedom. The cross section thickness property is requested form cross section model. The node numbering is anti-clockwise. The element features are summarized in :numref:`Tr1htsummary`. .. _Tr1htfig: .. tikz:: Tr1ht element - node and side numbering. \begin{tikzpicture}[scale=6,>=stealth] \tikzstyle{elemnode} = [draw,circle,inner sep=1,fill=white] \newcommand{\lcoordsys}[2]{ \begin{scope}[transform canvas={shift={#2},scale=0.5,rotate=#1}] \draw[->] (0,0.05) ++(-0.02,0) -- ++(0.2,0) node[above] {$x$}; \draw[->] (0,0.05) ++(0,-0.02) -- ++(0,0.1) node[right] {$y$}; \end{scope} } \draw[->] (-0.05,0) -- (0.8,0) node[above] {$x_g$}; \draw[->] (0,-0.05) -- (0,0.5) node[right] {$y_g$}; \draw[thick] (0.2,0.1) node[elemnode] {} node[below] {1} -- (0.7,0.2) node[elemnode] {} node[below] {2} node[blue,midway,below] {1} coordinate[midway] (e1) -- (0.4,0.5) node[elemnode] {} node[above] {3} node[blue,midway,above right] {2} coordinate[midway] (e2) -- (0.2,0.1) node[blue,midway,above left] {3} coordinate[midway] (e3); \lcoordsys{ 12}{(e1)}; \lcoordsys{135}{(e2)}; \lcoordsys{243}{(e3)}; \end{tikzpicture} .. table:: Tr1ht element summary :name: Tr1htsummary +--------------------------+----------------------------------------------------------------------------------------------+ | Keyword | Tr1ht | +--------------------------+----------------------------------------------------------------------------------------------+ | Description | triangular finite element with linear approximation for heat transfer problems | +--------------------------+----------------------------------------------------------------------------------------------+ | Parameters | :param:`NIP`: allows to change the default number of integration point used. | +--------------------------+----------------------------------------------------------------------------------------------+ | Unknowns | Single dof (T_f - temperature) is required in each node. | +--------------------------+----------------------------------------------------------------------------------------------+ | Approximation | Linear approximation of temperature. | +--------------------------+----------------------------------------------------------------------------------------------+ | Integration | Integration using one point gauss integration formula. | +--------------------------+----------------------------------------------------------------------------------------------+ | Loads | Body loads are supported. Boundary loads are supported and are computed using numerical | | | integration. The side numbering is following. Each i-th element side begins in i-th element | | | node and ends on next element node (i+1-th node or 1-st node, in the case of side number 3). | | | The local positive edge x-axis coincides with side direction, the positive local edge y-axis | | | is rotated 90 degrees anti-clockwise (see fig. (:ref:`Tr1htfig`)). | +--------------------------+----------------------------------------------------------------------------------------------+ | Features | - | +--------------------------+----------------------------------------------------------------------------------------------+ | CS properties | - | +--------------------------+----------------------------------------------------------------------------------------------+ | Status | | +--------------------------+----------------------------------------------------------------------------------------------+ | Tests/Examples | `tm/hydratingConcreteMat04.in | | | `_, | | | `tm/hydratingConcreteMat03.in | | | `_, | | | `tm/tmpatch45-1.in | | | `_, | | | `tm/hydratingConcreteMat01.in | | | `_, | | | `tm/hydratingConcreteMat06.in | | | `_, | | | `tm/hydratingConcreteMat02.in | | | `_, | | | `tm/hydratingConcreteMat07.in | | | `_, | | | `tm/hydratingConcreteMat05.in | | | `_, | | | `tm/tmpatch43-1.in | | | `_, | | | `tm/tmpatch43-3.in | | | `_ (and 1 | | | more) | +--------------------------+----------------------------------------------------------------------------------------------+ Tr1mt element ~~~~~~~~~~~~~ Isoparametric triangular finite element with linear approximation of moisture. Other features are the same as for Tr1ht in Section :ref:`Tr1ht`. Tr1hmt element ~~~~~~~~~~~~~~ Isoparametric triangular finite element with linear approximations of temperature and moisture. Other features are the same as for Tr1ht in Section :ref:`Tr1ht`. Tests/Examples: `tests/regression/tm/HeMoKunzel_1.in `_ .. _Quad1ht: Quad1ht element ~~~~~~~~~~~~~~~ Represents isoparametric four-node quadrilateral finite element for heat transfer problems. Each node has 1 degree of freedom. Problem should be defined in x,y plane. The cross section thickness property is requested form cross section model. The nodes should be numbered anti-clockwise (positive rotation around z-axis). The element features are summarized in :numref:`Quad1htsummary`. .. _Quad1htfig: .. tikz:: Quad1ht element. Node numbering, Side numbering and definition of local edge c.s.(a). \begin{tikzpicture}[scale=6,>=stealth] \tikzstyle{elemnode} = [draw,circle,inner sep=1,fill=white] \newcommand{\lcoordsys}[2]{ \begin{scope}[transform canvas={shift={#2},scale=0.5,rotate=#1}] \draw[->] (0,0.05) ++(-0.02,0) -- ++(0.2,0) node[above] {$x$}; \draw[->] (0,0.05) ++(0,-0.02) -- ++(0,0.1) node[right] {$y$}; \end{scope} } \draw[->] (-0.05,0) -- (0.8,0) node[above] {$x_g$}; \draw[->] (0,-0.05) -- (0,0.5) node[right] {$y_g$}; \draw[thick,xshift=-2] (0.2,0.1) -- (0.7,0.15) coordinate[midway] (e1) node[below,midway,blue] {1} node[elemnode] {} node[below right] {2} -- (0.8,0.45) coordinate[midway] (e2) node[right,midway,blue] {2} node[elemnode] {} node[above] {3} -- (0.3,0.5) coordinate[midway] (e3) node[above,midway,blue] {3} node[elemnode] {} node[above] {4} -- (0.2,0.1) coordinate[midway] (e4) node[left,midway,blue] {4} node[elemnode] {} node[below] {1}; \lcoordsys{ 7}{(e1)}; \lcoordsys{ 70}{(e2)}; \lcoordsys{175}{(e3)}; \lcoordsys{255}{(e4)}; \end{tikzpicture} .. table:: Quad1ht element summary :name: Quad1htsummary +--------------------------+----------------------------------------------------------------------------------------------+ | Keyword | Quad1ht | +--------------------------+----------------------------------------------------------------------------------------------+ | Description | Isoparametric four-node quadrilateral linear interpolation element for heat transfer | | | problems | +--------------------------+----------------------------------------------------------------------------------------------+ | Specific parameters | :optelemparam:`NIP{in}` | +--------------------------+----------------------------------------------------------------------------------------------+ | Parameters | :param:`NIP`: allows to change the default number of integration point used. | +--------------------------+----------------------------------------------------------------------------------------------+ | Unknowns | Single dof (T_f - temperature) is required in each node. | +--------------------------+----------------------------------------------------------------------------------------------+ | Approximation | Linear approximation of temperature. | +--------------------------+----------------------------------------------------------------------------------------------+ | Integration | Integration using gauss integration formula in 4 (the default), 9, or 16 integration points. | | | The default number of integration point used can be overloaded using :param:`NIP` parameter. | +--------------------------+----------------------------------------------------------------------------------------------+ | Loads | Body loads are supported. Boundary loads are supported and computed using numerical | | | integration. The side numbering is following. Each i-th element side begins in i-th element | | | node and ends on next element node (i+1-th node or 1-st node, in the case of side number 4). | | | The local positive edge x-axis coincides with side direction, the positive local edge y-axis | | | is rotated 90 degrees anti-clockwise (see fig. (:ref:`Quad1htfig`)). | +--------------------------+----------------------------------------------------------------------------------------------+ | Features | - | +--------------------------+----------------------------------------------------------------------------------------------+ | CS properties | - | +--------------------------+----------------------------------------------------------------------------------------------+ | Status | | +--------------------------+----------------------------------------------------------------------------------------------+ | Tests/Examples | `tmcemhyd/cemhyd01.in | | | `_, | | | `tm/tmpatch02.in | | | `_, | | | `tm/tmpatch01.in | | | `_, | | | `tm/tmpatch06.in | | | `_, | | | `tm/tmpatch11.in | | | `_, | | | `tm/tmpatch11dtf.in | | | `_, | | | `tm/tmpatch04.in | | | `_, | | | `tm/tmpatch05.in | | | `_, | | | `tm/tmpatch17.in | | | `_, | | | `tm/tmquad12.in | | | `_ (and 6 more) | +--------------------------+----------------------------------------------------------------------------------------------+ Quad1mt element ~~~~~~~~~~~~~~~ Isoparametric four-node quadrilateral finite element. Other features are the same as for Quad1ht in Section :ref:`Quad1ht`. Tests/Examples: `tests/regression/tm/nlisomoisture01.in `_, `tests/regression/tm/nlisomoisture02.in `_ Quad1hmt element ~~~~~~~~~~~~~~~~ Represents isoparametric four-node quadrilateral finite element for heat and mass (one constituent) transport problems. Two dofs (T_f - temperature and C_1 - concentration) are required in each node. Linear approximation of temperature and mass concentration. Other features are similar to Quad1 element, see section :ref:`Quad1ht`. .. _QQuad1ht: QQuad1ht element ~~~~~~~~~~~~~~~~ Represents isoparametric quadratic eight-node quadrilateral finite element for heat transfer problems. Each node has 1 degree of freedom. Problem should be defined in x,y plane. The cross section thickness property is requested form the cross section model. The nodes should be numbered anti-clockwise (positive rotation around z-axis), see fig. :ref:`qplanstrssfig`. The element has the same features as in Table :numref:`Quad1htsummary`. Tests/Examples: `tests/regression/tm/qquad01.in `_ QQuad1mt element ~~~~~~~~~~~~~~~~ Element for mass transport problems, see the parent element in sec. :ref:`QQuad1ht`. QQuad1hmt element ~~~~~~~~~~~~~~~~~ Element for heat and mass transport problems, see the parent element in sec. :ref:`QQuad1ht`.