FEA Periodic Boundaries - Revision history

Nairnj at 21:19, 2 June 2015

2015-06-02T21:19:24Z

← Older revision		Revision as of 21:19, 2 June 2015
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	* <tt>(dir)</tt> defines the periodic direction. [[NairnFEA]] allows periodicity in the <tt>x</tt> direction only, in the <tt>y</tt> direction only, or in both the <tt>x</tt> and <tt>y</tt> directions. For axisymmetric problems, periodicity is allowed in the <tt>Z</tt> direction only.		* <tt>(dir)</tt> defines the periodic direction. [[NairnFEA]] allows periodicity in the <tt>x</tt> direction only, in the <tt>y</tt> direction only, or in both the <tt>x</tt> and <tt>y</tt> directions. For axisymmetric problems, periodicity is allowed in the <tt>Z</tt> direction only.
	* The optional <tt>(dof1),(value1)</tt> and <tt>(dof2),(value2)</tt> in scripted files can fix one or two periodic boundary degrees of freedom. In each pair, the <tt>dof</tt> is the degree or freedom and <tt>value</tt> is the setting. The options for <tt>dof</tt> are:		* The optional <tt>(dof1),(value1)</tt> and <tt>(dof2),(value2)</tt> in scripted files can fix one or two periodic boundary degrees of freedom. In each pair, the <tt>dof</tt> is the degree or freedom and <tt>value</tt> is the setting. The options for <tt>dof</tt> are:
	*# <tt>Delta</tt> to set the displacement jump in that direction (in mm). When applied to the <tt>x</tt> direction, the global average strain is <ε<sub>xx</sub>> = <tt>Delta</tt>/Δx. When applied to the <tt>y</tt> direction, the global average strain is <ε<sub>yy</sub>> = <tt>Delta</tt>/Δy. When applied to the <tt>Z</tt> direction in axisymmetric analyses, the global average strain is <ε<sub>zz</sub>> = <tt>Delta</tt>/Δz. Here Δx, Δy, and Δz are the specimen lengths in those directions.		*# <tt>Delta</tt> to set the displacement jump in that direction (in [[ConsistentUnits Command#Legacy and Consistent Units\|length units]]). When applied to the <tt>x</tt> direction, the global average strain is <ε<sub>xx</sub>> = <tt>Delta</tt>/Δx. When applied to the <tt>y</tt> direction, the global average strain is <ε<sub>yy</sub>> = <tt>Delta</tt>/Δy. When applied to the <tt>Z</tt> direction in axisymmetric analyses, the global average strain is <ε<sub>zz</sub>> = <tt>Delta</tt>/Δz. Here Δx, Δy, and Δz are the specimen lengths in those directions.
	*# <tt>Slope</tt> defines the relative edge slopes between the two sides when there is one periodic direction (dimensioness). It is Δu<sub>s</sub>/Δy for <tt>x</tt> direction only and Δv<sub>s</sub>/Δx for <tt>y</tt> (or <tt>Z</tt>) direction only.		*# <tt>Slope</tt> defines the relative edge slopes between the two sides when there is one periodic direction (dimensioness). It is Δu<sub>s</sub>/Δy for <tt>x</tt> direction only and Δv<sub>s</sub>/Δx for <tt>y</tt> (or <tt>Z</tt>) direction only.
	*# <tt>Shear</tt> defines the shearing displacement jump difference between the two sides of the periodic direction (in mm) when both directions are periodic. It is Δu<sub>s</sub> for <tt>x</tt> direction setting and Δv<sub>s</sub> for <tt>y</tt> (or <tt>Z</tt>) direction setting. When periodic in both <tt>x</tt> and <tt>y</tt> directions, the average shear strain is <γ<sub>xy</sub>> = <tt>ShearX</tt>/Δy + <tt>ShearY</tt>/Δx. Here Δx and Δy are the specimen lengths in the two directions, <tt>ShearX</tt> is Δu<sub>s</sub>, and <tt>ShearY</tt> is Δv<sub>s</sub>.		*# <tt>Shear</tt> defines the shearing displacement jump difference between the two sides of the periodic direction (in [[ConsistentUnits Command#Legacy and Consistent Units\|length units]]) when both directions are periodic. It is Δu<sub>s</sub> for <tt>x</tt> direction setting and Δv<sub>s</sub> for <tt>y</tt> (or <tt>Z</tt>) direction setting. When periodic in both <tt>x</tt> and <tt>y</tt> directions, the average shear strain is <γ<sub>xy</sub>> = <tt>ShearX</tt>/Δy + <tt>ShearY</tt>/Δx. Here Δx and Δy are the specimen lengths in the two directions, <tt>ShearX</tt> is Δu<sub>s</sub>, and <tt>ShearY</tt> is Δv<sub>s</sub>.
	* In <tt>XML</tt> files, optional <tt>(value1)</tt> and <tt>(value2)</tt> set the displacement jump and rotation using <tt>delta</tt> and <tt>slope</tt>, <tt>shear</tt> attributes.		* In <tt>XML</tt> files, optional <tt>(value1)</tt> and <tt>(value2)</tt> set the displacement jump and rotation using <tt>delta</tt> and <tt>slope</tt>, <tt>shear</tt> attributes.

Nairnj: /* Input Commands */

2015-03-20T18:57:52Z

Input Commands

← Older revision		Revision as of 18:57, 20 March 2015
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	For periodicity to work, the edges of the specimen on the two ends of the periodic direction(s) must be orthognal to that direction, they must each have the same number of nodes, and the orthogonal coordinate (''e.g.'', the <tt>y</tt> coordinate for <tt>x</tt> periodicity, the <tt>x</tt> coordinate for <tt>y</tt> periodicity, or the <tt>R</tt> coordinate for <tt>Z</tt> periodicity) of each node on one side must match the corresponding node on the other side.		For periodicity to work, the edges of the specimen on the two ends of the periodic direction(s) must be orthognal to that direction, they must each have the same number of nodes, and the orthogonal coordinate (''e.g.'', the <tt>y</tt> coordinate for <tt>x</tt> periodicity, the <tt>x</tt> coordinate for <tt>y</tt> periodicity, or the <tt>R</tt> coordinate for <tt>Z</tt> periodicity) of each node on one side must match the corresponding node on the other side.

	Setting the periodic degrees of freedom for <tt>Delta</tt>, <tt>Slope</tt>, and <tt>Shear</tt> are optional. If they are not set, they are degrees of freedom in the problem (and can be found from output results). If they are set as boundary conditions, they can determine the average normal strains, edge rotations, and average shear strains. Finally, scripted commands can use <tt>Slope</tt> as a synonym from <tt>Shear</tt> and <tt>XML</tt> command can use a <tt>slope</tt> attribute as a synonym for the <tt>shear</tt> attribute. The code defines the appropriately depending on whether one or two directions are made periodic.		Setting the periodic degrees of freedom for <tt>Delta</tt>, <tt>Slope</tt>, and <tt>Shear</tt> are optional. If they are not set, they are degrees of freedom in the problem (and can be found from output results). If they are set as boundary conditions, they can determine the average normal strains, edge rotations, and average shear strains. Finally, scripted commands can use <tt>Slope</tt> as a synonym from <tt>Shear</tt> and <tt>XML</tt> command can use a <tt>slope</tt> attribute as a synonym for the <tt>shear</tt> attribute. The code defines the appropriately condition depending on whether one or two directions are made periodic.

	== Notes ==		== Notes ==

Nairnj: /* Input Commands */

2015-03-20T18:56:25Z

Input Commands

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	* The optional <tt>(dof1),(value1)</tt> and <tt>(dof2),(value2)</tt> in scripted files can fix one or two periodic boundary degrees of freedom. In each pair, the <tt>dof</tt> is the degree or freedom and <tt>value</tt> is the setting. The options for <tt>dof</tt> are:		* The optional <tt>(dof1),(value1)</tt> and <tt>(dof2),(value2)</tt> in scripted files can fix one or two periodic boundary degrees of freedom. In each pair, the <tt>dof</tt> is the degree or freedom and <tt>value</tt> is the setting. The options for <tt>dof</tt> are:
	*# <tt>Delta</tt> to set the displacement jump in that direction (in mm). When applied to the <tt>x</tt> direction, the global average strain is <ε<sub>xx</sub>> = <tt>Delta</tt>/Δx. When applied to the <tt>y</tt> direction, the global average strain is <ε<sub>yy</sub>> = <tt>Delta</tt>/Δy. When applied to the <tt>Z</tt> direction in axisymmetric analyses, the global average strain is <ε<sub>zz</sub>> = <tt>Delta</tt>/Δz. Here Δx, Δy, and Δz are the specimen lengths in those directions.		*# <tt>Delta</tt> to set the displacement jump in that direction (in mm). When applied to the <tt>x</tt> direction, the global average strain is <ε<sub>xx</sub>> = <tt>Delta</tt>/Δx. When applied to the <tt>y</tt> direction, the global average strain is <ε<sub>yy</sub>> = <tt>Delta</tt>/Δy. When applied to the <tt>Z</tt> direction in axisymmetric analyses, the global average strain is <ε<sub>zz</sub>> = <tt>Delta</tt>/Δz. Here Δx, Δy, and Δz are the specimen lengths in those directions.
	*# <tt>Shear</tt> defines the shearing displacement jump difference between the two sides of the periodic direction (in mm). When periodic in both <tt>x</tt> and <tt>y</tt> directions, the average shear strain is <γ<sub>xy</sub>> = <tt>ShearX</tt>/Δy + <tt>ShearY</tt>/Δx. Here Δx and Δy are the specimen lengths in the two directions, <tt>ShearX</tt> is Δu<sub>s</sub>, and <tt>ShearY</tt> is Δv<sub>s</sub>~~. When only one direction is periodic, the <tt>Shear</tt> variable describes a relative rotation of the two edges~~.		*# <tt>Slope</tt> defines the relative edge slopes between the two sides when there is one periodic direction (dimensioness). It is Δu<sub>s</sub>/Δy for <tt>x</tt> direction only and Δv<sub>s</sub>/Δx for <tt>y</tt> (or <tt>Z</tt>) direction only.
	* In <tt>XML</tt> files, optional <tt>(value1)</tt> and <tt>(value2)</tt> set the displacement jump and rotation using <tt>delta</tt> and <tt>shear</tt> attributes.		*# <tt>Shear</tt> defines the shearing displacement jump difference between the two sides of the periodic direction (in mm) when both directions are periodic. It is Δu<sub>s</sub> for <tt>x</tt> direction setting and Δv<sub>s</sub> for <tt>y</tt> (or <tt>Z</tt>) direction setting. When periodic in both <tt>x</tt> and <tt>y</tt> directions, the average shear strain is <γ<sub>xy</sub>> = <tt>ShearX</tt>/Δy + <tt>ShearY</tt>/Δx. Here Δx and Δy are the specimen lengths in the two directions, <tt>ShearX</tt> is Δu<sub>s</sub>, and <tt>ShearY</tt> is Δv<sub>s</sub>.
			* In <tt>XML</tt> files, optional <tt>(value1)</tt> and <tt>(value2)</tt> set the displacement jump and rotation using <tt>delta</tt> and <tt>slope</tt>, <tt>shear</tt> attributes.

	For periodicity to work, the edges of the specimen on the two ends of the periodic direction(s) must be orthognal to that direction, they must each have the same number of nodes, and the orthogonal coordinate (''e.g.'', the <tt>y</tt> coordinate for <tt>x</tt> periodicity, the <tt>x</tt> coordinate for <tt>y</tt> periodicity, or the <tt>R</tt> coordinate for <tt>Z</tt> periodicity) of each node on one side must match the corresponding node on the other side.		For periodicity to work, the edges of the specimen on the two ends of the periodic direction(s) must be orthognal to that direction, they must each have the same number of nodes, and the orthogonal coordinate (''e.g.'', the <tt>y</tt> coordinate for <tt>x</tt> periodicity, the <tt>x</tt> coordinate for <tt>y</tt> periodicity, or the <tt>R</tt> coordinate for <tt>Z</tt> periodicity) of each node on one side must match the corresponding node on the other side.

	Setting the periodic degrees of freedom for <tt>Delta</tt> and <tt>Shear</tt> are optional. If they are not set, they are degrees of freedom in the problem (and can be found from output results). If ~~the~~ are set as boundary conditions, they can determine the average normal strains, edge rotations, and average shear strains. Finally, scripted commands can use <tt>Slope</tt> as a synonym from <tt>Shear</tt> and <tt>XML</tt> command can use a <tt>slope</tt> attribute as a synonym for the <tt>shear</tt> attribute.		Setting the periodic degrees of freedom for <tt>Delta</tt>, <tt>Slope</tt>, and <tt>Shear</tt> are optional. If they are not set, they are degrees of freedom in the problem (and can be found from output results). If they are set as boundary conditions, they can determine the average normal strains, edge rotations, and average shear strains. Finally, scripted commands can use <tt>Slope</tt> as a synonym from <tt>Shear</tt> and <tt>XML</tt> command can use a <tt>slope</tt> attribute as a synonym for the <tt>shear</tt> attribute. The code defines the appropriately depending on whether one or two directions are made periodic.

	== Notes ==		== Notes ==

Nairnj: /* Theory */

2015-03-20T18:46:34Z

Theory

← Older revision		Revision as of 18:46, 20 March 2015
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	[[File:Periodic.jpg\|right]]		[[File:Periodic.jpg\|right]]
	The figure on the right shows a mesh of width Δx and height Δy in which the left and right edges are parallel to the <tt>y</tt> axis and each node on the left edge corresponds to a node on the right edge at the same <tt>y</tt> coordinate. If this structure is a piece on a large object that is periodic in the <tt>x</tt> direction, it means that the strains are periodic or that:		The figure on the right shows a mesh of width Δx and height Δy in which the left and right edges are parallel to the <tt>y</tt> axis and each node on the left edge corresponds to a node on the right edge at the same <tt>y</tt> coordinate. If this structure is a piece on a large object that is periodic in the <tt>x</tt> direction only, it means that the strains are periodic or that:


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	<math>v_i(\Delta x,y_i) = v_i(0,y_i) + v_1(\Delta x,y_1) - v_1(0,y_1) \qquad {\rm for}\ i=2,\ {\rm to}\ n</math>		<math>v_i(\Delta x,y_i) = v_i(0,y_i) + v_1(\Delta x,y_1) - v_1(0,y_1) \qquad {\rm for}\ i=2,\ {\rm to}\ n</math>

	These conditions are solved by using FEA method of Lagrange multipliers. All <tt>x</tt> displacements on the right are replaced by constraints as are all <tt>y</tt> (except v_1(Δx,y_1), which remains a degree of freedom). In addition, k<sub>1</sub> and k<sub>2</sub> are introduced as two new degrees of freedom. It is better to rewrite new degrees of freedom using		These conditions are solved by using FEA method of Lagrange multipliers. All <tt>x</tt> displacements on the right are replaced by constraints as are all <tt>y</tt> (except <math>v_1(\Delta x,y_1)</math>, which remains a degree of freedom). In addition, k<sub>1</sub> and k<sub>2</sub> are introduced as two new degrees of freedom. It is better to rewrite new degrees of freedom using


	<math>k_1 + k_2 y_i = \Delta u_n + {\Delta u_s\over \Delta y}(y_i - \left\langle y\right\rangle)</math>		<math>k_1 + k_2 y_i = \Delta u_n + {\Delta u_s\over \Delta y}(y_i - \left\langle y\right\rangle)</math>

	where <<tt>y</tt>> is the mean <tt>y</tt> on the edges. Physically, Δu<sub>n</sub> the mean displacement jump in the x direction across the modeled object, which results in an average <tt>x</tt> direction strain:		where <<tt>y</tt>> is the mean <tt>y</tt> on the edges. Physically, Δu<sub>n</sub> is the mean displacement jump in the x direction across the modeled object, which results in an average <tt>x</tt> direction strain:


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	<math>\left\langle \varepsilon_{yy}\right\rangle = {\Delta v_n\over \Delta y}</math>		<math>\left\langle \varepsilon_{yy}\right\rangle = {\Delta v_n\over \Delta y}</math>

	Similarly, Δv<sub>s</sub> the shear jump in the y direction or the difference in y direction jumps at the left and right of the object. If both directions are periodic, the average shear strain is		Similarly, Δv<sub>s</sub> the shear jump in the y direction or the difference in y direction jumps at the left and right of the object.

			If both directions are periodic, the analysis needs some modifications. The general displacement constraints between left and right or top and bottom edges can be written:


			<math>u_i(\Delta x,y_i) = u_i(0,y_i) + \left\langle \varepsilon_{xx}\right\rangle \Delta x = u_i(0,y_i) + \Delta u_n</math>


			<math>v_i(\Delta x,y_i) = v_i(0,y_i) + \left({\left\langle\gamma_{xy}\right\rangle\over 2} - \omega\right) \Delta x = v_i(0,y_i) + \Delta v_s</math>


			<math>u_i(x_i,\Delta y) = u_i(x_i,0) + \left({\left\langle \gamma_{xy}\right\rangle\over 2} + \omega\right) \Delta y = u_i(x_i,0) + \Delta u_s</math>


			<math>v_i(x_i,\Delta y) = v_i(x_i,0) + \left\langle \varepsilon_{yy}\right\rangle \Delta y = v_i(x_i,0) + \Delta v_n</math>

			where ω is a rigid body rotation. The average normal strains are as above. The average shear strain is

Nairnj: /* Input Commands */

2015-03-20T01:59:47Z

Input Commands

← Older revision		Revision as of 01:59, 20 March 2015
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	*# <tt>Delta</tt> to set the displacement jump in that direction (in mm). When applied to the <tt>x</tt> direction, the global average strain is <ε<sub>xx</sub>> = <tt>Delta</tt>/Δx. When applied to the <tt>y</tt> direction, the global average strain is <ε<sub>yy</sub>> = <tt>Delta</tt>/Δy. When applied to the <tt>Z</tt> direction in axisymmetric analyses, the global average strain is <ε<sub>zz</sub>> = <tt>Delta</tt>/Δz. Here Δx, Δy, and Δz are the specimen lengths in those directions.		*# <tt>Delta</tt> to set the displacement jump in that direction (in mm). When applied to the <tt>x</tt> direction, the global average strain is <ε<sub>xx</sub>> = <tt>Delta</tt>/Δx. When applied to the <tt>y</tt> direction, the global average strain is <ε<sub>yy</sub>> = <tt>Delta</tt>/Δy. When applied to the <tt>Z</tt> direction in axisymmetric analyses, the global average strain is <ε<sub>zz</sub>> = <tt>Delta</tt>/Δz. Here Δx, Δy, and Δz are the specimen lengths in those directions.
	*# <tt>Shear</tt> defines the shearing displacement jump difference between the two sides of the periodic direction (in mm). When periodic in both <tt>x</tt> and <tt>y</tt> directions, the average shear strain is <γ<sub>xy</sub>> = <tt>ShearX</tt>/Δy + <tt>ShearY</tt>/Δx. Here Δx and Δy are the specimen lengths in the two directions, <tt>ShearX</tt> is Δu<sub>s</sub>, and <tt>ShearY</tt> is Δv<sub>s</sub>. When only one direction is periodic, the <tt>Shear</tt> variable describes a relative rotation of the two edges.		*# <tt>Shear</tt> defines the shearing displacement jump difference between the two sides of the periodic direction (in mm). When periodic in both <tt>x</tt> and <tt>y</tt> directions, the average shear strain is <γ<sub>xy</sub>> = <tt>ShearX</tt>/Δy + <tt>ShearY</tt>/Δx. Here Δx and Δy are the specimen lengths in the two directions, <tt>ShearX</tt> is Δu<sub>s</sub>, and <tt>ShearY</tt> is Δv<sub>s</sub>. When only one direction is periodic, the <tt>Shear</tt> variable describes a relative rotation of the two edges.
	* In <tt>XML</tt> files, optional <tt>(value1)</tt> and <tt>(value2)</tt> set the displacement jump and rotation using <tt>delta</tt> and <tt>~~slope~~</tt> attributes.		* In <tt>XML</tt> files, optional <tt>(value1)</tt> and <tt>(value2)</tt> set the displacement jump and rotation using <tt>delta</tt> and <tt>shear</tt> attributes.

	For periodicity to work, the edges of the specimen on the two ends of the periodic direction(s) must be orthognal to that direction, they must each have the same number of nodes, and the orthogonal coordinate (''e.g.'', the <tt>y</tt> coordinate for <tt>x</tt> periodicity, the <tt>x</tt> coordinate for <tt>y</tt> periodicity, or the <tt>R</tt> coordinate for <tt>Z</tt> periodicity) of each node on one side must match the corresponding node on the other side.		For periodicity to work, the edges of the specimen on the two ends of the periodic direction(s) must be orthognal to that direction, they must each have the same number of nodes, and the orthogonal coordinate (''e.g.'', the <tt>y</tt> coordinate for <tt>x</tt> periodicity, the <tt>x</tt> coordinate for <tt>y</tt> periodicity, or the <tt>R</tt> coordinate for <tt>Z</tt> periodicity) of each node on one side must match the corresponding node on the other side.

Nairnj: /* Input Commands */

2015-03-20T01:59:14Z

Input Commands

← Older revision		Revision as of 01:59, 20 March 2015
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	* The optional <tt>(dof1),(value1)</tt> and <tt>(dof2),(value2)</tt> in scripted files can fix one or two periodic boundary degrees of freedom. In each pair, the <tt>dof</tt> is the degree or freedom and <tt>value</tt> is the setting. The options for <tt>dof</tt> are:		* The optional <tt>(dof1),(value1)</tt> and <tt>(dof2),(value2)</tt> in scripted files can fix one or two periodic boundary degrees of freedom. In each pair, the <tt>dof</tt> is the degree or freedom and <tt>value</tt> is the setting. The options for <tt>dof</tt> are:
	*# <tt>Delta</tt> to set the displacement jump in that direction (in mm). When applied to the <tt>x</tt> direction, the global average strain is <ε<sub>xx</sub>> = <tt>Delta</tt>/Δx. When applied to the <tt>y</tt> direction, the global average strain is <ε<sub>yy</sub>> = <tt>Delta</tt>/Δy. When applied to the <tt>Z</tt> direction in axisymmetric analyses, the global average strain is <ε<sub>zz</sub>> = <tt>Delta</tt>/Δz. Here Δx, Δy, and Δz are the specimen lengths in those directions.		*# <tt>Delta</tt> to set the displacement jump in that direction (in mm). When applied to the <tt>x</tt> direction, the global average strain is <ε<sub>xx</sub>> = <tt>Delta</tt>/Δx. When applied to the <tt>y</tt> direction, the global average strain is <ε<sub>yy</sub>> = <tt>Delta</tt>/Δy. When applied to the <tt>Z</tt> direction in axisymmetric analyses, the global average strain is <ε<sub>zz</sub>> = <tt>Delta</tt>/Δz. Here Δx, Δy, and Δz are the specimen lengths in those directions.
	*# <tt>Shear</tt> defines the shearing displacement jump difference between the two sides of the periodic direction (in mm). When periodic in both <tt>x</tt> and <tt>y</tt> directions, the average shear strain is <γ<sub>xy</sub>> = <tt>ShearX</tt>/Δy + <tt>ShearY</tt>/Δx. Here Δx and Δy are the specimen lengths in the two directions, <tt>ShearX</tt> is Δu<sub>s</sub>, and <tt>ShearY</tt> is Δv<sub>s</sub>. When only one direction is periodic, the <tt>~~Slope~~</tt> variable describes a relative rotation of the two edges.		*# <tt>Shear</tt> defines the shearing displacement jump difference between the two sides of the periodic direction (in mm). When periodic in both <tt>x</tt> and <tt>y</tt> directions, the average shear strain is <γ<sub>xy</sub>> = <tt>ShearX</tt>/Δy + <tt>ShearY</tt>/Δx. Here Δx and Δy are the specimen lengths in the two directions, <tt>ShearX</tt> is Δu<sub>s</sub>, and <tt>ShearY</tt> is Δv<sub>s</sub>. When only one direction is periodic, the <tt>Shear</tt> variable describes a relative rotation of the two edges.
	* In <tt>XML</tt> files, optional <tt>(value1)</tt> and <tt>(value2)</tt> set the displacement jump and rotation using <tt>delta</tt> and <tt>slope</tt> attributes.		* In <tt>XML</tt> files, optional <tt>(value1)</tt> and <tt>(value2)</tt> set the displacement jump and rotation using <tt>delta</tt> and <tt>slope</tt> attributes.

Nairnj: /* Input Commands */

2015-03-20T01:58:51Z

Input Commands

← Older revision		Revision as of 01:58, 20 March 2015
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	* The optional <tt>(dof1),(value1)</tt> and <tt>(dof2),(value2)</tt> in scripted files can fix one or two periodic boundary degrees of freedom. In each pair, the <tt>dof</tt> is the degree or freedom and <tt>value</tt> is the setting. The options for <tt>dof</tt> are:		* The optional <tt>(dof1),(value1)</tt> and <tt>(dof2),(value2)</tt> in scripted files can fix one or two periodic boundary degrees of freedom. In each pair, the <tt>dof</tt> is the degree or freedom and <tt>value</tt> is the setting. The options for <tt>dof</tt> are:
	*# <tt>Delta</tt> to set the displacement jump in that direction (in mm). When applied to the <tt>x</tt> direction, the global average strain is <ε<sub>xx</sub>> = <tt>Delta</tt>/Δx. When applied to the <tt>y</tt> direction, the global average strain is <ε<sub>yy</sub>> = <tt>Delta</tt>/Δy. When applied to the <tt>Z</tt> direction in axisymmetric analyses, the global average strain is <ε<sub>zz</sub>> = <tt>Delta</tt>/Δz. Here Δx, Δy, and Δz are the specimen lengths in those directions.		*# <tt>Delta</tt> to set the displacement jump in that direction (in mm). When applied to the <tt>x</tt> direction, the global average strain is <ε<sub>xx</sub>> = <tt>Delta</tt>/Δx. When applied to the <tt>y</tt> direction, the global average strain is <ε<sub>yy</sub>> = <tt>Delta</tt>/Δy. When applied to the <tt>Z</tt> direction in axisymmetric analyses, the global average strain is <ε<sub>zz</sub>> = <tt>Delta</tt>/Δz. Here Δx, Δy, and Δz are the specimen lengths in those directions.
	*# <tt>Shear</tt> defines the shearing displacement jump difference between the two sides of the periodic direction (in mm). When periodic in both <tt>x</tt> and <tt>y</tt> directions, the average shear strain is <γ<sub>xy</sub>> = <tt>ShearX</tt>/Δy + <tt>ShearY</tt>/Δx. Here Δx and Δy are the specimen lengths in the two directions, <tt> ~~SlopeX~~</tt> is Δu<sub>s</sub>, and <tt>~~SlopeY~~</tt> is Δv<sub>s</sub>. When only one direction is periodic, the <tt>Slope</tt> variable describes a relative rotation of the two edges.		*# <tt>Shear</tt> defines the shearing displacement jump difference between the two sides of the periodic direction (in mm). When periodic in both <tt>x</tt> and <tt>y</tt> directions, the average shear strain is <γ<sub>xy</sub>> = <tt>ShearX</tt>/Δy + <tt>ShearY</tt>/Δx. Here Δx and Δy are the specimen lengths in the two directions, <tt>ShearX</tt> is Δu<sub>s</sub>, and <tt>ShearY</tt> is Δv<sub>s</sub>. When only one direction is periodic, the <tt>Slope</tt> variable describes a relative rotation of the two edges.
	* In <tt>XML</tt> files, optional <tt>(value1)</tt> and <tt>(value2)</tt> set the displacement jump and rotation using <tt>delta</tt> and <tt>slope</tt> attributes.		* In <tt>XML</tt> files, optional <tt>(value1)</tt> and <tt>(value2)</tt> set the displacement jump and rotation using <tt>delta</tt> and <tt>slope</tt> attributes.

Nairnj: /* Input Commands */

2015-03-20T01:57:30Z

Input Commands

← Older revision		Revision as of 01:57, 20 March 2015
Line 77:		Line 77:
	* The optional <tt>(dof1),(value1)</tt> and <tt>(dof2),(value2)</tt> in scripted files can fix one or two periodic boundary degrees of freedom. In each pair, the <tt>dof</tt> is the degree or freedom and <tt>value</tt> is the setting. The options for <tt>dof</tt> are:		* The optional <tt>(dof1),(value1)</tt> and <tt>(dof2),(value2)</tt> in scripted files can fix one or two periodic boundary degrees of freedom. In each pair, the <tt>dof</tt> is the degree or freedom and <tt>value</tt> is the setting. The options for <tt>dof</tt> are:
	*# <tt>Delta</tt> to set the displacement jump in that direction (in mm). When applied to the <tt>x</tt> direction, the global average strain is <ε<sub>xx</sub>> = <tt>Delta</tt>/Δx. When applied to the <tt>y</tt> direction, the global average strain is <ε<sub>yy</sub>> = <tt>Delta</tt>/Δy. When applied to the <tt>Z</tt> direction in axisymmetric analyses, the global average strain is <ε<sub>zz</sub>> = <tt>Delta</tt>/Δz. Here Δx, Δy, and Δz are the specimen lengths in those directions.		*# <tt>Delta</tt> to set the displacement jump in that direction (in mm). When applied to the <tt>x</tt> direction, the global average strain is <ε<sub>xx</sub>> = <tt>Delta</tt>/Δx. When applied to the <tt>y</tt> direction, the global average strain is <ε<sub>yy</sub>> = <tt>Delta</tt>/Δy. When applied to the <tt>Z</tt> direction in axisymmetric analyses, the global average strain is <ε<sub>zz</sub>> = <tt>Delta</tt>/Δz. Here Δx, Δy, and Δz are the specimen lengths in those directions.
	*# <tt>~~Slope~~</tt> defines the shearing displacement jump difference between the two sides of the periodic direction (in mm). When periodic in both <tt>x</tt> and <tt>y</tt> directions, the average shear strain is <γ<sub>xy</sub>> = <tt>~~SlopeX~~</tt>/Δy + <tt>~~SlopeY~~</tt>/Δx. Here Δx and Δy are the specimen lengths in the two directions, <tt> SlopeX</tt> is Δu<sub>s</sub>, and <tt>SlopeY</tt> is Δv<sub>s</sub>. When only one direction is periodic, the <tt>Slope</tt> variable describes a relative rotation of the two edges.		*# <tt>Shear</tt> defines the shearing displacement jump difference between the two sides of the periodic direction (in mm). When periodic in both <tt>x</tt> and <tt>y</tt> directions, the average shear strain is <γ<sub>xy</sub>> = <tt>ShearX</tt>/Δy + <tt>ShearY</tt>/Δx. Here Δx and Δy are the specimen lengths in the two directions, <tt> SlopeX</tt> is Δu<sub>s</sub>, and <tt>SlopeY</tt> is Δv<sub>s</sub>. When only one direction is periodic, the <tt>Slope</tt> variable describes a relative rotation of the two edges.
	* In <tt>XML</tt> files, optional <tt>(value1)</tt> and <tt>(value2)</tt> set the displacement jump and rotation using <tt>delta</tt> and <tt>slope</tt> attributes.		* In <tt>XML</tt> files, optional <tt>(value1)</tt> and <tt>(value2)</tt> set the displacement jump and rotation using <tt>delta</tt> and <tt>slope</tt> attributes.

	For periodicity to work, the edges of the specimen on the two ends of the periodic direction(s) must be orthognal to that direction, they must each have the same number of nodes, and the orthogonal coordinate (''e.g.'', the <tt>y</tt> coordinate for <tt>x</tt> periodicity, the <tt>x</tt> coordinate for <tt>y</tt> periodicity, or the <tt>R</tt> coordinate for <tt>Z</tt> periodicity) of each node on one side must match the corresponding node on the other side.		For periodicity to work, the edges of the specimen on the two ends of the periodic direction(s) must be orthognal to that direction, they must each have the same number of nodes, and the orthogonal coordinate (''e.g.'', the <tt>y</tt> coordinate for <tt>x</tt> periodicity, the <tt>x</tt> coordinate for <tt>y</tt> periodicity, or the <tt>R</tt> coordinate for <tt>Z</tt> periodicity) of each node on one side must match the corresponding node on the other side.

	Setting the periodic degrees of freedom for <tt>Delta</tt> and <tt>~~Slope~~</tt> are optional. If they are not set, they are degrees of freedom in the problem (and can be found from output results). If the are set as boundary conditions, they can determine the average normal strains, edge rotations, and average shear strains. Finally, scripted commands can use <tt>~~Shear~~</tt> as a synonym from <tt>~~Slope~~</tt> and <tt>XML</tt> command can use a <tt>~~shear~~</tt> attribute as a synonym for the <tt>~~slope~~</tt> attribute.		Setting the periodic degrees of freedom for <tt>Delta</tt> and <tt>Shear</tt> are optional. If they are not set, they are degrees of freedom in the problem (and can be found from output results). If the are set as boundary conditions, they can determine the average normal strains, edge rotations, and average shear strains. Finally, scripted commands can use <tt>Slope</tt> as a synonym from <tt>Shear</tt> and <tt>XML</tt> command can use a <tt>slope</tt> attribute as a synonym for the <tt>shear</tt> attribute.

	== Notes ==		== Notes ==

Nairnj: /* Input Commands */

2015-03-20T01:56:08Z

Input Commands

← Older revision		Revision as of 01:56, 20 March 2015
Line 77:		Line 77:
	* The optional <tt>(dof1),(value1)</tt> and <tt>(dof2),(value2)</tt> in scripted files can fix one or two periodic boundary degrees of freedom. In each pair, the <tt>dof</tt> is the degree or freedom and <tt>value</tt> is the setting. The options for <tt>dof</tt> are:		* The optional <tt>(dof1),(value1)</tt> and <tt>(dof2),(value2)</tt> in scripted files can fix one or two periodic boundary degrees of freedom. In each pair, the <tt>dof</tt> is the degree or freedom and <tt>value</tt> is the setting. The options for <tt>dof</tt> are:
	*# <tt>Delta</tt> to set the displacement jump in that direction (in mm). When applied to the <tt>x</tt> direction, the global average strain is <ε<sub>xx</sub>> = <tt>Delta</tt>/Δx. When applied to the <tt>y</tt> direction, the global average strain is <ε<sub>yy</sub>> = <tt>Delta</tt>/Δy. When applied to the <tt>Z</tt> direction in axisymmetric analyses, the global average strain is <ε<sub>zz</sub>> = <tt>Delta</tt>/Δz. Here Δx, Δy, and Δz are the specimen lengths in those directions.		*# <tt>Delta</tt> to set the displacement jump in that direction (in mm). When applied to the <tt>x</tt> direction, the global average strain is <ε<sub>xx</sub>> = <tt>Delta</tt>/Δx. When applied to the <tt>y</tt> direction, the global average strain is <ε<sub>yy</sub>> = <tt>Delta</tt>/Δy. When applied to the <tt>Z</tt> direction in axisymmetric analyses, the global average strain is <ε<sub>zz</sub>> = <tt>Delta</tt>/Δz. Here Δx, Δy, and Δz are the specimen lengths in those directions.
	*# <tt>Slope</tt> defines the shearing displacement jump difference between the two sides of the periodic direction (in mm). When periodic in both <tt>x</tt> and <tt>y</tt> directions, the average shear strain is <γ<sub>xy</sub>> = <tt>SlopeX</tt>/Δy + <tt>~~SlopeX~~</tt>/Δx. Here Δx and Δy are the specimen lengths in the two directions, <tt> SlopeX</tt> is Δu<sub>s</sub>, and <tt>SlopeY</tt> is Δv<sub>s</sub>. When only one direction is periodic, the <tt>Slope</tt> variable describes a relative rotation of the two edges.		*# <tt>Slope</tt> defines the shearing displacement jump difference between the two sides of the periodic direction (in mm). When periodic in both <tt>x</tt> and <tt>y</tt> directions, the average shear strain is <γ<sub>xy</sub>> = <tt>SlopeX</tt>/Δy + <tt>SlopeY</tt>/Δx. Here Δx and Δy are the specimen lengths in the two directions, <tt> SlopeX</tt> is Δu<sub>s</sub>, and <tt>SlopeY</tt> is Δv<sub>s</sub>. When only one direction is periodic, the <tt>Slope</tt> variable describes a relative rotation of the two edges.
	* In <tt>XML</tt> files, optional <tt>(value1)</tt> and <tt>(value2)</tt> set the displacement jump and rotation using <tt>delta</tt> and <tt>slope</tt> attributes.		* In <tt>XML</tt> files, optional <tt>(value1)</tt> and <tt>(value2)</tt> set the displacement jump and rotation using <tt>delta</tt> and <tt>slope</tt> attributes.

Nairnj: /* Input Commands */

2015-03-20T01:55:48Z

Input Commands

← Older revision		Revision as of 01:55, 20 March 2015
Line 77:		Line 77:
	* The optional <tt>(dof1),(value1)</tt> and <tt>(dof2),(value2)</tt> in scripted files can fix one or two periodic boundary degrees of freedom. In each pair, the <tt>dof</tt> is the degree or freedom and <tt>value</tt> is the setting. The options for <tt>dof</tt> are:		* The optional <tt>(dof1),(value1)</tt> and <tt>(dof2),(value2)</tt> in scripted files can fix one or two periodic boundary degrees of freedom. In each pair, the <tt>dof</tt> is the degree or freedom and <tt>value</tt> is the setting. The options for <tt>dof</tt> are:
	*# <tt>Delta</tt> to set the displacement jump in that direction (in mm). When applied to the <tt>x</tt> direction, the global average strain is <ε<sub>xx</sub>> = <tt>Delta</tt>/Δx. When applied to the <tt>y</tt> direction, the global average strain is <ε<sub>yy</sub>> = <tt>Delta</tt>/Δy. When applied to the <tt>Z</tt> direction in axisymmetric analyses, the global average strain is <ε<sub>zz</sub>> = <tt>Delta</tt>/Δz. Here Δx, Δy, and Δz are the specimen lengths in those directions.		*# <tt>Delta</tt> to set the displacement jump in that direction (in mm). When applied to the <tt>x</tt> direction, the global average strain is <ε<sub>xx</sub>> = <tt>Delta</tt>/Δx. When applied to the <tt>y</tt> direction, the global average strain is <ε<sub>yy</sub>> = <tt>Delta</tt>/Δy. When applied to the <tt>Z</tt> direction in axisymmetric analyses, the global average strain is <ε<sub>zz</sub>> = <tt>Delta</tt>/Δz. Here Δx, Δy, and Δz are the specimen lengths in those directions.
	*# <tt>Slope</tt> defines the shearing displacement jump difference ~~slopes~~ between the two sides of the periodic direction. When periodic in both <tt>x</tt> and <tt>y</tt> directions, the average shear strain is <γ<sub>xy</sub>> = <tt>SlopeX</tt>/Δy + <tt>SlopeX</tt>/Δx. Here Δx and Δy are the specimen lengths in the two directions, <tt> SlopeX</tt> is Δu<sub>s</sub>, and <tt>SlopeY</tt> is Δv<sub>s</sub>. When only one direction is periodic, the <tt>Slope</tt> variable describes a relative rotation of the two edges.		*# <tt>Slope</tt> defines the shearing displacement jump difference between the two sides of the periodic direction (in mm). When periodic in both <tt>x</tt> and <tt>y</tt> directions, the average shear strain is <γ<sub>xy</sub>> = <tt>SlopeX</tt>/Δy + <tt>SlopeX</tt>/Δx. Here Δx and Δy are the specimen lengths in the two directions, <tt> SlopeX</tt> is Δu<sub>s</sub>, and <tt>SlopeY</tt> is Δv<sub>s</sub>. When only one direction is periodic, the <tt>Slope</tt> variable describes a relative rotation of the two edges.
	* In <tt>XML</tt> files, optional <tt>(value1)</tt> and <tt>(value2)</tt> set the displacement jump and rotation using <tt>delta</tt> and <tt>slope</tt> attributes.		* In <tt>XML</tt> files, optional <tt>(value1)</tt> and <tt>(value2)</tt> set the displacement jump and rotation using <tt>delta</tt> and <tt>slope</tt> attributes.