Detailed Description

Author: Daniel Wirtz

Date: 2011-12-05

New in 0.6:: (Daniel Wirtz, 2011-12-05) Added this class.

This class is part of the framework

KerMor - Model Order Reduction using Kernels

Homepage http://www.morepas.org/software/index.html
Documentation http://www.morepas.org/software/kermor/index.html
License KerMor license conditions

Definition at line 19 of file CurvedBeam.m.

Public Member Functions
	CurvedBeam (models.BaseFullModel model, material, pointsidx)

function M =	getLocalMassMatrix ()
	Berechnet lokale Steifigkeits- und Massenmatrix eines gekr�mmten Timoshenko-Balkens (Viertelkreis) (numerisch mit speziell gewonnenen Ansatzfunktionen) More...

function K =	getLocalStiffnessMatrix ()
	Berechnet lokale Steifigkeits- und Massenmatrix eines gekr�mmten Timoshenko-Balkens (Viertelkreis) (numerisch mit speziell gewonnenen Ansatzfunktionen) More...

function f =	getLocalForceMatrix ()
	Berechnet lokale Steifigkeits- und Massenmatrix eines gekr�mmten Timoshenko-Balkens (Viertelkreis) (numerisch mit speziell gewonnenen Ansatzfunktionen) More...

function [ K , R , U_pot ] =	getLocalTangentials (u)

function B =	circle_connect_matrix ()

function N =	circle_shape_functions (s, B)
	Wertet die Basisfunktionen f�r ein Kreiselement aus: Auf dem Element werden konstante Strains angenommen => DGLs der Form x' = Ax + c2 m�ssen gel�st werden. x = (u1, u2, u3, theta1, theta2, theta3). Es ergibt sich eine L�sung der Form: x(s) = C(s) * c. Wobei C 6x12 und c ein Vektor mit Konstanten der L�nge 12 ist. (c = [x(0); c2]) Um nun Basisfunktionen zu generieren m�ssen die L�sungen x(s) mit den Werten an den beiden Enden des Elements verbunden werden: v = [x(0); x(L)] = [C(0); C(L)] * c =: inv(B) * c. More...

function	plot (p, u1, u2, col1, col2, plot_options)
	Zeichnet Timoshenko Kreisbogen Die Ansatzfunktionen werden dabei an N Zwischenstellen ausgewertet, d.h. N=0 ist zul�ssig Anfangs- und Endpunkte (x, y, z), sowie Anfangs- und Endverschiebung (lokal!) (u, v, w, phi, psi, theta) sind gegeben. Colormap-Indices f�r Anfangs-/Endpunkt col1/col2 sind gegeben, Farbe wird linear interpoliert centerline = 2; % Art der Mittellinie (0: keine, 1: d�nn, 2: dick mit Endmarkierung) More...

Public Member Functions inherited from models.beam.Beam
	Beam (models.BaseFullModel model, material, pointsidx)

function globIdx =	getGlobalIndices ()
	Returns the global indices in the vector of DoFs for this element. More...

Public Member Functions inherited from models.beam.StructureElement
	StructureElement (models.BaseFullModel model, material, pointsidx)

virtual function [ M , K , f , K , R , U_pot , globIdx ] =	getGlobalIndices (gravity, this, u, this)

Public Attributes
	pc

	R

	angle

	Fren

	B

	B3

	B4

	T_block1

	T_block2

Public Attributes inherited from models.beam.Beam
	split
	Speichert den anteil des jeweiligen Elements an der Gesamtsysteml�nge. More...

Public Attributes inherited from models.beam.StructureElement
	PointsIdx
	Punkt-Index-Array. More...

	Material
	Material vector. More...

	Length
	Indizes (lokal pro Knoten) in die die lokalen Matrizen assembliert werden Konvention: Freiheitsgrade pro Knoten (u1, u2, u3, phi1, phi2, phi3, T, [...]) MatrixDofIndices; L�nge des Elements. More...

	Model
	The model that contains the structure element. More...

	T
	Transformationsmatrix f�r das lokale Koordinatensystem. More...

	c
	Effektive Stoffkonstanten. More...

Public Attributes inherited from handle
	addlistener
	Creates a listener for the specified event and assigns a callback function to execute when the event occurs. More...

	notify
	Broadcast a notice that a specific event is occurring on a specified handle object or array of handle objects. More...

	delete
	Handle object destructor method that is called when the object's lifecycle ends. More...

	disp
	Handle object disp method which is called by the display method. See the MATLAB disp function. More...

	display
	Handle object display method called when MATLAB software interprets an expression returning a handle object that is not terminated by a semicolon. See the MATLAB display function. More...

	findobj
	Finds objects matching the specified conditions from the input array of handle objects. More...

	findprop
	Returns a meta.property objects associated with the specified property name. More...

	fields
	Returns a cell array of string containing the names of public properties. More...

	fieldnames
	Returns a cell array of string containing the names of public properties. See the MATLAB fieldnames function. More...

	isvalid
	Returns a logical array in which elements are true if the corresponding elements in the input array are valid handles. This method is Sealed so you cannot override it in a handle subclass. More...

	eq
	Relational functions example. See details for more information. More...

	transpose
	Transposes the elements of the handle object array. More...

	permute
	Rearranges the dimensions of the handle object array. See the MATLAB permute function. More...

	reshape
	hanges the dimensions of the handle object array to the specified dimensions. See the MATLAB reshape function. More...

	sort
	ort the handle objects in any array in ascending or descending order. More...

Protected Member Functions
function	initialize ()

Protected Member Functions inherited from models.beam.Beam
function	initialize ()
	this.c_theta = this.Material(9); this.kappa = this.Material(10); this.alphaA = this.Material(11) * this.Material(2) * this.Material(3); % alphaAE More...

Additional Inherited Members
Protected Attributes inherited from models.beam.StructureElement
	TG
	c_theta = []; kappa = []; alphaA = []; The global transformation matrix (?) More...

Constructor & Destructor Documentation

models.beam.CurvedBeam.CurvedBeam	(	models.BaseFullModel	model,
			material,
			pointsidx
	)

Definition at line 71 of file CurvedBeam.m.

References initialize(), and pc.

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Member Function Documentation

function B = models.beam.CurvedBeam.circle_connect_matrix ( )

Definition at line 327 of file CurvedBeam.m.

References B, circle_shape_functions(), and models.beam.StructureElement.Length.

Referenced by initialize().

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function N = models.beam.CurvedBeam.circle_shape_functions	(	s,
		B
	)

Wertet die Basisfunktionen f�r ein Kreiselement aus: Auf dem Element werden konstante Strains angenommen => DGLs der Form x' = Ax + c2 m�ssen gel�st werden. x = (u1, u2, u3, theta1, theta2, theta3). Es ergibt sich eine L�sung der Form: x(s) = C(s) * c. Wobei C 6x12 und c ein Vektor mit Konstanten der L�nge 12 ist. (c = [x(0); c2]) Um nun Basisfunktionen zu generieren m�ssen die L�sungen x(s) mit den Werten an den beiden Enden des Elements verbunden werden: v = [x(0); x(L)] = [C(0); C(L)] * c =: inv(B) * c.

Definition at line 335 of file CurvedBeam.m.

References B, and R.

Referenced by circle_connect_matrix(), getLocalForceMatrix(), getLocalMassMatrix(), getLocalStiffnessMatrix(), getLocalTangentials(), and plot().

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function f = models.beam.CurvedBeam.getLocalForceMatrix ( )

Berechnet lokale Steifigkeits- und Massenmatrix eines gekr�mmten Timoshenko-Balkens (Viertelkreis) (numerisch mit speziell gewonnenen Ansatzfunktionen)

c1 = E*I c2 = G*It c3 = E*A c4 = G*As c5 = rho*A c6 = rho*I c7 = rho*It

Definition at line 168 of file CurvedBeam.m.

References B, models.beam.StructureElement.c, circle_shape_functions(), models.beam.StructureElement.Length, models.beam.Material.q_plus, models.beam.StructureElement.T, t, and models.beam.StructureElement.TG.

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function M = models.beam.CurvedBeam.getLocalMassMatrix ( )

Berechnet lokale Steifigkeits- und Massenmatrix eines gekr�mmten Timoshenko-Balkens (Viertelkreis) (numerisch mit speziell gewonnenen Ansatzfunktionen)

c1 = E*I c2 = G*It c3 = E*A c4 = G*As c5 = rho*A c6 = rho*I c7 = rho*It

Definition at line 78 of file CurvedBeam.m.

References B, models.beam.StructureElement.c, circle_shape_functions(), models.beam.StructureElement.Length, t, and models.beam.StructureElement.TG.

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function K = models.beam.CurvedBeam.getLocalStiffnessMatrix ( )

Berechnet lokale Steifigkeits- und Massenmatrix eines gekr�mmten Timoshenko-Balkens (Viertelkreis) (numerisch mit speziell gewonnenen Ansatzfunktionen)

c1 = E*I c2 = G*It c3 = E*A c4 = G*As c5 = rho*A c6 = rho*I c7 = rho*It

Definition at line 120 of file CurvedBeam.m.

References B, B3, B4, models.beam.StructureElement.c, circle_shape_functions(), models.beam.StructureElement.Length, t, and models.beam.StructureElement.TG.

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function [K , R , U_pot ] = models.beam.CurvedBeam.getLocalTangentials ( u )

Definition at line 201 of file CurvedBeam.m.

References B, B3, B4, models.beam.StructureElement.c, circle_shape_functions(), F, models.beam.StructureElement.Length, R, t, and models.beam.StructureElement.TG.

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function models.beam.CurvedBeam.initialize ( )

protected

Definition at line 512 of file CurvedBeam.m.

References angle, B, B3, B4, models.beam.StructureElement.c, circle_connect_matrix(), Fren, models.beam.StructureElement.Length, models.beam.StructureElement.Material, models.beam.StructureElement.Model, pc, models.beam.StructureElement.PointsIdx, R, models.beam.StructureElement.T, t, T_block1, T_block2, and models.beam.StructureElement.TG.

Referenced by CurvedBeam().

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function models.beam.CurvedBeam.plot	(	p,
		u1,
		u2,
		col1,
		col2,
		plot_options
	)

Zeichnet Timoshenko Kreisbogen Die Ansatzfunktionen werden dabei an N Zwischenstellen ausgewertet, d.h. N=0 ist zul�ssig Anfangs- und Endpunkte (x, y, z), sowie Anfangs- und Endverschiebung (lokal!) (u, v, w, phi, psi, theta) sind gegeben. Colormap-Indices f�r Anfangs-/Endpunkt col1/col2 sind gegeben, Farbe wird linear interpoliert centerline = 2; % Art der Mittellinie (0: keine, 1: d�nn, 2: dick mit Endmarkierung)

crosssection = 0; % Querschnitte (0: keine, 1: nach Theorie 1. Ordn, 2: Theorie 2. Ordn, sonst: exakt rotiert)