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framelinearanalysis.m
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% Ç êýñéá äïìÞ äåäïìÝíùí ôïõ ðñïãñÜììáôïò åßíáé ðñïóâÜóéìç áðü ðáíôïý
global data;
% =================================================================== XML PARSER
% Ôï Octave áðáéôåß ôç âéâëéïèÞêç Apache Xerces ãéá íá öïñôþóåé, áðïèçêåýóåé
% êáé êÜíåé ëåêôéêÞ áíÜëõóç, áñ÷åßá xml.
% Ç âéâëéïèÞêç äåí õðÜñ÷åé óôï Octave. Ï ÷ñÞóôçò ðñÝðåé íá ôçí êáôåâÜóåé.
javaaddpath("xercesImpl-2.12.0-sp1.jar");
javaaddpath("xml-apis-ext-1.3.04.jar");
% Ôï Octave áðáéôåß ôï io ðáêÝôï ãéá íá öïñôþóåé, áðïèçêåýóåé êáé êÜíåé ëåêôéêÞ
% áíÜëõóç, áñ÷åßá xml.
% Ãéá ôçí åãêáôÜóôáóÞ ôïõ åêôåëïýìå ôçí åíôïëÞ `pkg install -forge io`
pkg load io;
% ÅëÝã÷åé áí Ýíá xml element Ý÷åé ôï üíïìá ðïõ èÝëïõìå.
% in: node: xml element ãéá Ýëåã÷ï
% in: name: Ôï üíïìá ðïõ èÝëïõìå íá Ý÷åé ôï xml element
% error: Áí äåí Ý÷åé ôï üíïìá ðïõ èÝëïõìå
function parseCheckElementName(node, name)
if ~strcmp(node.getNodeName, name)
error(["ÁíáìÝíïíôáí ", name, " element, âñÝèçêå ", node.getNodeName]);
endif;
endfunction
% Ôï êåßìåíï åßíáé Ýãêõñï xml üíïìá
% in: str Ôï êåßìåíï
% out: is Ôï êåßìåíï åßíáé Ýãêõñï xml üíïìá, êáôÜëëçëï ãéá @id
function is = isXmlName(str)
is = ~isempty(regexp(str, '^[A-Za-z_Á-Ùá-ù¢-¿Ü-þúÀûÀò][\w-.]*$'));
endfunction
% ËåêôéêÞ áíÜëõóç åíüò xml element ìå üíïìá material
% in: node: Ôï xml element ôïõ õëéêïý.
% out: material: Octave äïìÞ õëéêïý.
% error: ÓöÜëìá êáôÜ ôçí ëåêôéêÞ áíÜëõóç Þ ìç Ýãêõñá äåäïìÝíá.
function material = parseMaterial(node)
parseCheckElementName(node, "material");
material.id = node.getAttribute("id"); % Ôï material@id åßíáé ðñïáéñåôéêü
% ÓôáèåñÜ ôïõ Young
material.E = str2num(node.getAttribute("E"));
if (length(material.E) ~= 1 || material.E <= 0)
error(["material ìå ìç Ýãêõñï @E=", num2str(material.E)]);
endif;
% Ëüãïò Poisson
v = str2num(node.getAttribute("v"));
if (length(v))
if (length(v) ~= 1 || v <= 0 || v > 0.5)
error(["material ìå ìç Ýãêõñï @v=", num2str(v)]);
endif;
material.v = v;
endif
endfunction
% ËåêôéêÞ áíÜëõóç åíüò xml element "O"
% in: node: Ôï xml element ôçò äéáôïìÞò.
% out: section: Octave äïìÞ äéáôïìÞò.
% error: ÓöÜëìá êáôÜ ôçí ëåêôéêÞ áíÜëõóç Þ ìç Ýãêõñá äåäïìÝíá.
function section = parseFrameSectionO(node)
section.diameter = str2num(node.getAttribute("diameter"));
if (length(section.diameter) == 1)
if (section.diameter < 0)
error(["ÐñÝðåé frame_section@diameter > 0, äçëáäÞ ", num2str(section.diameter), " > 0"]);
endif;
elseif (length(section.diameter) == 2)
if (section.diameter(1) <= section.diameter(2) || section.diameter(2) < 0)
error(["ÐñÝðåé 0 <= frame_section@diameter(2) < frame_section@diameter(1), äçëáäÞ 0 < ", ...
num2str(section.diameter(2)), " < ", num2str(section.diameter(1))]);
endif;
else
error(["Ï áñéèìüò äéáìÝôñùí ìðïñåß íá åßíáé Ýíáò (óõìðáãÞò) Þ äýï (åîùôåñéêüò - åóùôåñéêüò). ÂñÝèçêáí ", ...
num2str(length(section.diameter))]);
endif
endfunction
% ËåêôéêÞ áíÜëõóç åíüò xml element "generic"
% in: node: Ôï xml element ôçò äéáôïìÞò.
% out: section: Octave äïìÞ äéáôïìÞò.
% error: ÓöÜëìá êáôÜ ôçí ëåêôéêÞ áíÜëõóç Þ ìç Ýãêõñá äåäïìÝíá.
function section = parseFrameSectionGeneric(node)
A = str2num(node.getAttribute("A"));
if (length(A))
if (length(A) > 1 || A <= 0) error(["ÐñÝðåé generic@Iy > 0, äçëáäÞ ", num2str(Iy), " > 0"]); endif
section.A = A;
endif
Iy = str2num(node.getAttribute("Iy"));
if (length(Iy))
if (length(Iy) > 1 || Iy <= 0) error(["ÐñÝðåé generic@Iy > 0, äçëáäÞ ", num2str(Iy), " > 0"]); endif
section.Iy = Iy;
endif
Iz = str2num(node.getAttribute("Iz"));
if (length(Iz))
if (length(Iz) > 1 || Iz <= 0) error(["ÐñÝðåé generic@Iz > 0, äçëáäÞ ", num2str(Iz), " > 0"]); endif
section.Iz = Iz;
endif
It = str2num(node.getAttribute("It"));
if (length(It))
if (length(It) > 1 || It <= 0) error(["ÐñÝðåé generic@It > 0, äçëáäÞ ", num2str(It), " > 0"]); endif
section.It = It;
endif
Cs = str2num(node.getAttribute("Cs"));
if (length(Cs))
if (length(Cs) > 1 || Cs <= 0) error(["ÐñÝðåé generic@Cs > 0, äçëáäÞ ", num2str(Cs), " > 0"]); endif
section.Cs = Cs;
endif
It_S = str2num(node.getAttribute("It_S"));
if (length(It_S))
if (length(It_S) > 1 || It_S <= 0) error(["ÐñÝðåé generic@It_S > 0, äçëáäÞ ", num2str(It_S), " > 0"]); endif
section.It_S = It_S;
endif
ay = str2num(node.getAttribute("ay"));
if (length(ay))
if (length(ay) > 1 || ay < 1) error(["ÐñÝðåé generic@ay > 1, äçëáäÞ ", num2str(ay), " > 1"]); endif
section.ay = ay;
endif
az = str2num(node.getAttribute("az"));
if (length(az))
if (length(az) > 1 || az < 1) error(["ÐñÝðåé generic@az > 1, äçëáäÞ ", num2str(az), " > 1"]); endif
section.az = az;
endif
endfunction
% ËåêôéêÞ áíÜëõóç åíüò xml element ìå üíïìá frame_section
% in: node: Ôï xml element ôçò äéáôïìÞò.
% out: section: Octave äïìÞ äéáôïìÞò.
% error: ÓöÜëìá êáôÜ ôçí ëåêôéêÞ áíÜëõóç Þ ìç Ýãêõñá äåäïìÝíá.
function section = parseFrameSection(node)
type = node.getNodeName;
switch(type)
case "O" section = parseFrameSectionO(node);
case "generic" section = parseFrameSectionGeneric(node);
otherwise error(['Ìç õðïóôçñéæüìåíïò ôýðïò äéáôïìÞò ', type]);
endswitch;
section.type = type;
section.id = node.getAttribute("id"); % Ôï section@id åßíáé ðñïáéñåôéêü
endfunction
% ÓõíôåôáãìÝíåò åíüò óçìåßïõ ðïõ äéáâÜæïíôáé áðü êåßìåíï ÷ùñéóìÝíï ìå êåíÜ
% in: str: Êåßìåíï ðïõ ðåñéÝ÷åé óõíôåôáãìÝíåò ÷ùñéóìÝíåò ìå êåíÜ.
% out: coords: Ïé óõíôåôáãìÝíåò ôïõ óçìåßïõ.
% error: ÓöÜëìá êáôÜ ôçí ëåêôéêÞ áíÜëõóç Þ ìç Ýãêõñá äåäïìÝíá.
function coords = parseCoords(str)
if (strcmp(str, "+x")) coords = [1, 0, 0];
elseif (strcmp(str, "+y")) coords = [0, 1, 0];
elseif (strcmp(str, "+z")) coords = [0, 0, 1];
elseif (strcmp(str, "-x")) coords = [-1, 0, 0];
elseif (strcmp(str, "-y")) coords = [0, -1, 0];
elseif (strcmp(str, "-z")) coords = [0, 0, -1];
else
coords = str2num(str);
if (length(coords) ~= 2 && length(coords) ~= 3)
error(["Ïé óõíôåôáãìÝíåò ðñÝðåé íá åßíáé 2 Þ 3 êáé âñÝèçêáí ", num2str(length(coords))]);
elseif (length(coords) == 2) coords(3) = 0; % ÐñïóèÞêç 3çò óõíôåôáãìÝíçò
endif
endif
endfunction
% Ôïðéêü óýóôçìá óõíôåôáãìÝíùí ðïõ äéáâÜæåôáé áðü êåßìåíï ÷ùñéóìÝíï ìå êåíÜ
% in: str: Êåßìåíï ðïõ ðåñéÝ÷åé óõíôåôáãìÝíåò áîüíùí ôïõ óõóôÞìáôïò ÷ùñéóìÝíåò ìå êåíÜ.
% out: lcs: Ï ðßíáêáò ôïõ ôïðéêïý óõóôÞìáôïò óõíôåôáãìÝíùí Þ empty áí äåí õðÜñ÷åé.
% error: ÓöÜëìá êáôÜ ôçí ëåêôéêÞ áíÜëõóç Þ ìç Ýãêõñá äåäïìÝíá.
function lcs = parseCoordinateSystem(str)
lcs = str2num(str);
if (length(lcs) == 6) % 3d ôïðéêü óýóôçìá óõíôåôáãìÝíùí
x = lcs(1:3);
y = lcs(4:6);
n = norm(x);
if (~n) error("Ìçäåíéêü äéÜíõóìá Üîïíá x óå ôïðéêü óýóôçìá óõíôåôáãìÝíùí"); endif
x /= n;
n = norm(y);
if (~n) error("Ìçäåíéêü äéÜíõóìá Üîïíá y óå ôïðéêü óýóôçìá óõíôåôáãìÝíùí"); endif
y /= n;
z = cross(x, y);
n = norm(z);
if (n < 0.02)
error(["Ôï äéÜíõóìá ôïõ Üîïíá y ðñÝðåé íá Ý÷åé ãùíßá ôïõëÜ÷éóôïí 1.145° ìå ôïí Üîïíá x óå ôïðéêü óýóôçìá óõíôåôáãìÝíùí: y=", ...
num2str(y), " èxy=", num2str(asin(n * 180 / pi)), "°"]);
endif
z /= n;
y = cross(z, x);
lcs = [x; y; z];
elseif (length(lcs) == 2) % 2d ôïðéêü óýóôçìá óõíôåôáãìÝíùí ðïõ èá ãßíåé 3d
n = norm(lcs);
if (~n) error("Ìçäåíéêü äéÜíõóìá Üîïíá x óå ôïðéêü óýóôçìá óõíôåôáãìÝíùí"); endif
lcs /= n;
lcs(3) = 0;
z = [0, 0, 1];
lcs = [lcs; cross(z, lcs); z];
else
error(["¸íá óýóôçìá óõíôåôáãìÝíùí ïñßæåôáé áðü 6 Þ 2 óõíéóôþóåò êáé âñÝèçêáí ", ...
num2str(length(lcs))]);
endif
endfunction
% ËåêôéêÞ áíÜëõóç åíüò xml element ðïõ ðåñéÝ÷åé öïñôéï (ð.÷. force Þ moment)
% in: node: Ôï xml element ôïõ óôïé÷åßïõ.
% out: load: Octave äïìÞ óôïé÷åßïõ.
% error: ÓöÜëìá êáôÜ ôçí ëåêôéêÞ áíÜëõóç Þ ìç Ýãêõñá äåäïìÝíá.
function load = parseLoad(node)
% Åßíáé äýíáìç Þ ñïðÞ;
str = node.getNodeName;
switch(str)
case "force" load.force = true;
case "moment" load.force = false;
otherwise error(["Ôï öïñôßï ìðïñåß íá åßíáé Þ force Þ moment êáé âñÝèçêå: ", str]);
endswitch
load.id = node.getAttribute("id"); % Ôï node@id åßíáé ðñïáéñåôéêü
load.coords = parseCoords(node.getAttribute("direction")); % Êáôåýèõíóç öïñôßïõ
n = norm(load.coords);
if (~n) error("Ìçäåíéêü äéÜíõóìá êáôåýèõíóçò öïñôßïõ"); endif
% Ôï ìÝôñï ôïõ öïñôßïõ (ðñïáéñåôéêü)
% Ç ëïãéêÞ åßíáé íá äþóïõìå ìéá êáôåýèõíóç óôï öïñôßï ôÝôïéá þóôå íá ìáò âïëåýïõí ôá íïõìåñá êáé
% áêïëïýèùò íá äþóïõìå ôï ìÝôñï ôïõ öïñôßïõ. Áí ðáñáëåßðåôáé, ç êáôåýèõíóç ôïõ öïñôßïõ ðåñéëáìâÜíåé
% ôï ìÝôñï
if (node.hasAttribute("magnitude"))
magnitude = str2num(node.getAttribute("magnitude"));
switch(length(magnitude))
case 1
load.coords *= magnitude / n;
case 2 % ÊáôáíåìçìÝíï öïñôßï ìå êáôáíïìÞ ôñáðåæßïõ
load.coords /= n;
load.magnitude = magnitude;
otherwise
error(["Ôï ìÝãåèïò öïñôßïõ åßíáé ðñïáéñåôéêü, êáé âñÝèçêå ìç Ýãêõñï: ", num2str(magnitude)]);
endswitch
endif
% Ôï öïñôßï åöáñìüæåôáé óå óýóôçìá óõíôåôáãìÝíùí ôïðéêü Þ êáèïëéêü
% ÁöïñÜ ìüíï ìÝëç (óôïé÷åßá). Óå êüìâïõò áãíïåßôáé.
load.lcs = true; % default ôéìÞ
if (node.hasAttribute("coordinate_system"))
str = node.getAttribute("coordinate_system");
switch(str)
case "global"
load.lcs = false;
case "local"
otherwise
error(["ôï óýóôçìá óõíôåôáãìÝíùí ôïõ öïñôßïõ åßíáé Þ global Þ local, êáé âñÝèçêå: ", str]);
endswitch
endif
endfunction
% ÅðéóôñÝöåé ôï index åíüò óôïé÷åßïõ áðü ôéò öïñôùìÝíåò ïìÜäåò óôïé÷åßùí
% in: m: Ôï üíïìá (@id) Þ ôï index áðü Ýíá óôïé÷åßï ìéáò ïìÜäáò óôïé÷åßùí.
% in: what: Ôï åßäïò ôçò ïìÜäáò óôïé÷åßùí ð.÷. "section" Þ "material" Þ "load" Þ "node".
% out: idx: Ôï index ôïõ óôïé÷åßïõ óôçí ïìÜäá óôïé÷åßùí.
function idx = getItemIndexFromData(m, what)
global data; % Ôá äåäïìÝíá ôïõ öïñÝá, üðùò Ý÷ïõí öïñôùèåß ìÝ÷ñé ôþñá.
whats = [what, "s"];
if (isnumeric(m)) idxd = m; state = true;
else [idxd, state] = str2num(m);
endif
idx = uint32(idxd);
if (~state)
if (isfield(data.map.(whats), m))
idx = data.map.(whats).(m);
else
error(["ÅóöáëìÝíç áíáöïñÜ óå üíïìá ", what, ": ", m]);
endif
elseif (length(idx) ~= 1 || idx > length(data.(whats)) || idx != idxd)
error(["ÅóöáëìÝíç áíáöïñÜ óå index ", what, ": ", num2str(m)]);
endif
endfunction
% ÅðéóôñÝöåé Ýíá óôïé÷åßï áðü ôéò öïñôùìÝíåò ïìÜäåò óôïé÷åßùí
% in: m: Ôï üíïìá (@id) Þ ôï index áðü Ýíá óôïé÷åßï ìéáò ïìÜäáò óôïé÷åßùí.
% in: what: Ôï åßäïò ôçò ïìÜäáò óôïé÷åßùí ð.÷. "section" Þ "material" Þ "load" Þ "node".
% out: item: Ôï óôïé÷åßï áðü ôçí ïìÜäá óôïé÷åßùí.
function item = getItemFromData(m, what)
global data; % Ôá äåäïìÝíá ôïõ öïñÝá, üðùò Ý÷ïõí öïñôùèåß ìÝ÷ñé ôþñá.
item = data.([what, "s"]){getItemIndexFromData(m, what)};
endfunction
% ÅðéóôñÝöåé ëßóôá ìå ôá indices óôïé÷åßùí áðü ôéò öïñôùìÝíåò ïìÜäåò óôïé÷åßùí
% in: m: Ôá ïíüìáôá (@id) Þ ôá indices áðü Ýíá áñéèìü óôïé÷åßùí ìéáò ïìÜäáò óôïé÷åßùí.
% in: what: Ôï åßäïò ôçò ïìÜäáò óôïé÷åßùí ð.÷. "section" Þ "material" Þ "load" Þ "node".
% out: idx: Ëßóôá ìå ôá indices ôùí óôïé÷åßùí óôçí ïìÜäá óôïé÷åßùí.
function idx = getItemsIndicesFromData(m, what)
n = strsplit(m, " ");
idx = [];
for i = n
idx = [idx, getItemIndexFromData(i{1}, what)];
endfor
endfunction
% ÅðéóôñÝöåé ôá óôïé÷åßá áðü ôéò öïñôùìÝíåò ïìÜäåò óôïé÷åßùí
% in: m: Ôá ïíüìáôá (@id) Þ ôá indices áðü Ýíá áñéèìü óôïé÷åßùí ìéáò ïìÜäáò óôïé÷åßùí.
% in: what: Ôï åßäïò ôçò ïìÜäáò óôïé÷åßùí ð.÷. "section" Þ "material" Þ "load" Þ "node".
% out: items: Ëßóôá ìå ôá óôïé÷åßá óôçí ïìÜäá óôïé÷åßùí.
function items = getItemsFromData(m, what)
n = strsplit(m, " ");
items = {};
for i = n
items{length(items) + 1} = getItemFromData(i{1}, what);
endfor
endfunction
% ËåêôéêÞ áíÜëõóç åíüò xml element ìå üíïìá node
% in: node: Ôï xml element ôïõ êüìâïõ.
% out: nodE: Octave äïìÞ êüìâïõ.
% error: ÓöÜëìá êáôÜ ôçí ëåêôéêÞ áíÜëõóç Þ ìç Ýãêõñá äåäïìÝíá.
function nodE = parseNode(node)
global data;
parseCheckElementName(node, "node");
nodE.id = node.getAttribute("id"); % Ôï node@id åßíáé ðñïáéñåôéêü
% ÓõíôåôáãìÝíåò êüìâïõ. Ïñßæïíôáé Þ áíôéãñÜöïíôáé áðü Üëëïí.
% ÁíôéãñÜöïíôáé áðü Üëëïí üôáí Ý÷ïõìå ð.÷. åóùôåñéêÞ åëåõèÝñùóç.
b1 = node.hasAttribute("coords"); b2 = node.hasAttribute("clone_coords");
if (b1 && b2 || ~b1 && ~b2)
error("Ï node ðñÝðåé íá Ý÷åé áêñéâþò Ýíá áðü @coords êáé @clone_coords");
end
if (node.hasAttribute("coords"))
nodE.coords = parseCoords(node.getAttribute("coords")); % ÓõíôåôáãìÝíåò êüìâïõ
else
nodE.coords = getItemFromData(node.getAttribute("clone_coords"), "node").coords;
endif
% Åðéêüìâéá öïñôßá
if (node.hasAttribute("loads"))
loads = getItemsIndicesFromData(node.getAttribute("loads"), "load");
for i = loads
if (isfield(data.loads{i}, "magnitude"))
error(["Áðïäüèçêå ôï ôñáðåæßùò êáôáíåìçìÝíï öïñôßï ", num2str(i), " óå êüìâï"]);
endif
endfor
else loads = [];
endif
if (node.hasAttribute("clone_loads"))
loads = [loads, getItemFromData(node.getAttribute("clone_loads"), "node").loads];
endif
if (length(loads)) nodE.loads = loads; endif;
endfunction
% Êïéíüò êþäéêáò ëåêôéêÞò áíÜëõóçò ðñéóìáôéêþí óôïé÷åßùí
% Äåò parseBar() êáé parseBeam()
function element = parsePrismaticCommon(node)
element.material = getItemIndexFromData(node.getAttribute("material"), "material");
element.section = getItemIndexFromData(node.getAttribute("section"), "frame_section");
element.nodes = getItemsIndicesFromData(node.getAttribute("nodes"), "node");
if (length(element.nodes) ~= 2)
error(["Ç äïêüò Ý÷åé 2 êüìâïõò, âñÝèçêáí ", num2str(length(element.nodes))]);
endif
if (node.hasAttribute("initial_loads"))
element.initial_load = str2num(node.getAttribute("initial_loads"));
endif
endfunction
% ËåêôéêÞ áíÜëõóç åíüò xml element ìå üíïìá bar
% in: node: Ôï xml element ôïõ óôïé÷åßïõ.
% out: element: Octave äïìÞ óôïé÷åßïõ.
% error: ÓöÜëìá êáôÜ ôçí ëåêôéêÞ áíÜëõóç Þ ìç Ýãêõñá äåäïìÝíá.
function element = parseBar(node)
element = parsePrismaticCommon(node);
element.type = uint16(0); % bar type
% ¸ëåã÷ïò ôùí ðñïöïñôßóåùí íá åßíáé ìßá ôéìÞ ìüíï
if (isfield(element, "initial_load"))
if (length(element.initial_load) ~= 1)
error(["Ç ñÜâäïò Ý÷åé ìéá ôéìÞ ãéá ðñïöüñôéóç, âñÝèçêáí ", ...
num2str(length(element.initial_load))]);
endif
endif
endfunction
% ËåêôéêÞ áíÜëõóç åíüò xml element ìå üíïìá beam
% in: node: Ôï xml element ôïõ óôïé÷åßïõ.
% out: element: Octave äïìÞ óôïé÷åßïõ.
% error: ÓöÜëìá êáôÜ ôçí ëåêôéêÞ áíÜëõóç Þ ìç Ýãêõñá äåäïìÝíá.
function element = parseBeam(node)
element = parsePrismaticCommon(node);
element.type = uint16(3); % beam type
% ¸ëåã÷ïò ôùí ðñïöïñôßóåùí
if (isfield(element, "initial_load"))
switch(length(element.initial_load))
case 3 element.initial_load = [element.initial_load(1:2) 0 0 0 element.initial_load(3) 0];
case 6 element.initial_load(7) = 0;
case 7
otherwise
error(["Ç äïêüò ìðïñåß íá Ý÷åé 3, 6 Þ 7 ôéìÝò ãéá ðñïöüñôéóç, âñÝèçêáí ", ...
num2str(length(element.initial_load))]);
endswitch
endif
% Äéåýèõíóç z
if (node.hasAttribute("z_axis"))
element.axisZ = parseCoords(node.getAttribute("z_axis"));
n = norm(element.axisZ);
if (~n) error("Ç äéåýèõíóç beam@z_axis âñÝèçêå ìçäåíéêÞ"); endif
element.axisZ /= n;
endif
% ÊáôáíåìçìÝíá öïñôßá
if (node.hasAttribute("distributed_loads"))
element.distributed_loads = getItemsIndicesFromData(node.getAttribute("distributed_loads"), "load");
endif
% ÓôñÝâëùóç
element.warp = false;
if (node.hasAttribute("warp"))
w = node.getAttribute("warp");
switch(w)
case "yes" element.warp = true;
case "no"
otherwise error(["Ç äïêüò áí Ý÷åé @warp ðñÝðåé íá åßíáé yes Þ no, âñÝèçêå: ", w]);
endswitch
endif
endfunction
% ËåêôéêÞ áíÜëõóç åíüò xml element ìå üíïìá spring
% in: node: Ôï xml element ôïõ óôïé÷åßïõ.
% out: element: Octave äïìÞ óôïé÷åßïõ.
% error: ÓöÜëìá êáôÜ ôçí ëåêôéêÞ áíÜëõóç Þ ìç Ýãêõñá äåäïìÝíá.
function element = parseSpring(node)
global data; % Ôá äåäïìÝíá ôïõ öïñÝá, üðùò Ý÷ïõí öïñôùèåß ìÝ÷ñé ôþñá.
type = node.getAttribute("type");
switch(type)
case, "linear"
element.type = uint16(1); % linear spring type
case "torsion"
element.type = uint16(2); % torsion spring type
otherwise
error(["Ôï åëáôÞñéï ðñÝðåé Ý÷åé @type linear Þ torsion, âñÝèçêå ", type]);
endswitch
element.K = str2num(node.getAttribute("K"));
if (length(element.K) ~= 1)
error(["Ôï åëáôÞñéï Ý÷åé ìéá óôáèåñÜ Ê, âñÝèçêáí ", num2str(length(element.K))]);
endif
element.nodes = getItemsIndicesFromData(node.getAttribute("nodes"), "node");
if (length(element.nodes) ~= 1 && length(element.nodes) ~= 2)
error(["Ôï åëáôÞñéï Ý÷åé 1 Þ 2 êüìâïõò, âñÝèçêáí ", num2str(length(element.nodes))]);
endif
% @direction: Áí õðÜñ÷åé Þ åßíáé óôñïöéêü åëáôÞñéï Þ åßíáé ãñáììéêü êáé ïé 2 êüìâïé ôáõôßæïíôáé.
% åéäÜëëùò ç êáôåýèõíóç åßíáé áðü ôïí ðñþôï óôï äåýôåñï êüìâï.
if (length(element.nodes) == 2)
element.direction = data.nodes(element.nodes(2)).coords - data.nodes(element.nodes(1)).coords;
n = norm(element.direction);
endif
if (node.hasAttribute("direction") || length(element.nodes) == 1 || element.type == 2 || ~n)
element.direction = parseCoords(node.getAttribute("direction"));
n = norm(element.direction);
if (~n) error("Ìçäåíéêü äéÜíõóìá êáôåýèõíóçò åëáôçñßïõ"); endif
endif
element.direction /= n; % ìïíáäéáßï
if (node.hasAttribute("initial_loads"))
element.initial_load = str2num(node.getAttribute("initial_loads"));
if (length(element.initial_load) ~= 1)
error(["Ôï åëáôÞñéï Ý÷åé ìéá ôéìÞ ãéá ðñïöüñôéóç, âñÝèçêáí ", ...
num2str(length(element.initial_load))]);
endif
endif
endfunction
% ËåêôéêÞ áíÜëõóç åíüò xml element ðïõ åßíáé óôïé÷åßï ðåðåñáóìÝíùí óôïé÷åßùí
% in: node: Ôï xml element ôïõ óôïé÷åßïõ.
% out: element: Octave äïìÞ óôïé÷åßïõ.
% error: ÓöÜëìá êáôÜ ôçí ëåêôéêÞ áíÜëõóç Þ ìç Ýãêõñá äåäïìÝíá.
function element = parseElement(node)
% Åðåîåñãáóßá óôïé÷åßïõ ìå âÜóç ôïí ôýðï ôïõ
switch(node.getNodeName)
case "bar" element = parseBar(node);
case "spring" element = parseSpring(node);
case "beam" element = parseBeam(node);
otherwise error(["Ìç õðïóôçñéæüìåíïò ôýðïò óôïé÷åßïõ: ", node.getNodeName]);
endswitch
element.id = node.getAttribute("id"); % Ôï node@id åßíáé ðñïáéñåôéêü
endfunction
% ËåêôéêÞ áíÜëõóç åíüò xml attribute ðïõ åßíáé äÝóìåõóç åíüò êáé ìüíï DoF
% Ìðïñåß íá åßíáé "yes", "no", áñéèìüò Þ íá ðáñáëåßðåôáé.
% Áí ï DoF åßíáé äåóìåõìÝíïò, óôç ëßóôá restraint.dofs ðñïóèÝôåé ôï æåõãÜñé
% index ôïõ DoF êáé ôçí ôéìÞ ôçò äÝóìåõóçò.
% in: node: Ôï xml element ôïõ óôïé÷åßïõ.
% in: name: Ôï üíïìá ôïõ xml attribute ôïõ DoF.
% in/out: restraint: Ôï áíôéêåßìåíï ôçò äÝóìåõóçò.
% in: index: Ôï index ôïõ DoF óôïí êüìâï. ð.÷. ï disp_y åßíáé 2.
function restraint = parseRestraintDOF(node, name, restraint, index)
if (~node.hasAttribute(name)) return; endif
c = node.getAttribute(name);
switch(c)
case "no" return;
case "yes" a = 0;
otherwise
a = str2num(c);
if (length(a) ~= 1) error(["Ìç áðïäåêôÞ ôéìÞ äÝóìåõóçò ", name, ": ", c]); endif
endswitch
% ÅðéëÝãåôáé áõôü ôï áíÜóôñïöï format ãéáôß ç for áðáñéèìåß óôÞëåò(!) áíôß ãéá ãñáììÝò
restraint.dofs = [restraint.dofs, [index; a]];
endfunction
% ËåêôéêÞ áíÜëõóç åíüò xml element ðïõ åßíáé êáôáíáãêáóìüò (óôÞñéîç)
% in: node: Ôï xml element ôïõ óôïé÷åßïõ.
% out: restraint: Octave äïìÞ óôïé÷åßïõ.
% error: ÓöÜëìá êáôÜ ôçí ëåêôéêÞ áíÜëõóç Þ ìç Ýãêõñá äåäïìÝíá.
function restraint = parseRestraint(node)
parseCheckElementName(node, "restraint");
restraint.id = node.getAttribute("id"); % Ôï node@id åßíáé ðñïáéñåôéêü
restraint.nodes = getItemsIndicesFromData(node.getAttribute("nodes"), "node");
if (~length(restraint.nodes)) error("Ç äÝóìåõóç ðñÝðåé íá Ý÷åé ôïõëÜ÷éóôïí Ýíá êüìâï"); endif
% Ôïðéêü óýóôçìá óõíôåôáãìÝíùí (ðñïáéñåôéêü)
if (node.hasAttribute("local_coordinate_system"))
restraint.lcs = parseCoordinateSystem(node.getAttribute("local_coordinate_system"));
endif
% Äåóìåýóåéò âáèìþí åëåõèåñßáò
restraint.dofs = [];
restraint = parseRestraintDOF(node, "disp_x", restraint, 1);
restraint = parseRestraintDOF(node, "disp_y", restraint, 2);
restraint = parseRestraintDOF(node, "disp_z", restraint, 3);
restraint = parseRestraintDOF(node, "rot_x", restraint, 4);
restraint = parseRestraintDOF(node, "rot_y", restraint, 5);
restraint = parseRestraintDOF(node, "rot_z", restraint, 6);
restraint = parseRestraintDOF(node, "warp", restraint, 6);
endfunction
% ËåêôéêÞ áíÜëõóç åíüò xml element ðïõ åßíáé åîáíáãêáóìüò
% in: node: Ôï xml element ôïõ óôïé÷åßïõ.
% out: constraint: Octave äïìÞ óôïé÷åßïõ.
% error: ÓöÜëìá êáôÜ ôçí ëåêôéêÞ áíÜëõóç Þ ìç Ýãêõñá äåäïìÝíá.
function constraint = parseConstraint(node)
parseCheckElementName(node, "constraint");
constraint.id = node.getAttribute("id"); % Ôï node@id åßíáé ðñïáéñåôéêü
% Ôïðéêü óýóôçìá óõíôåôáãìÝíùí (ðñïáéñåôéêü)
if (node.hasAttribute("local_coordinate_system"))
constraint.lcs = parseCoordinateSystem(node.getAttribute("local_coordinate_system"));
endif
% Öüñôùóç ôùí êüìâùí ôùí DoF
nodes = getItemsIndicesFromData(node.getAttribute("nodes"), "node");
ii = length(nodes);
if (~ii) error("Ç äÝóìåõóç ðñÝðåé íá Ý÷åé ôïõëÜ÷éóôïí Ýíá êüìâï"); endif
% ÊáôáãñáöÞ üëùí ôùí DoFs óå óõíäõáóìü ìå ôïõò êüìâïõò ôïõò
dofs = strsplit(node.getAttribute("dofs"), " ");
i = 1; % index óôïí äåóìåõìÝíï êüìâï ðïõ èá öïñôùèåß ðéï êÜôù
constraint.dofs = [];
for dof = dofs
switch(dof{1})
case "disp_x" constraint.dofs = [constraint.dofs, [nodes(i); 1]];
case "disp_y" constraint.dofs = [constraint.dofs, [nodes(i); 2]];
case "disp_z" constraint.dofs = [constraint.dofs, [nodes(i); 3]];
case "rot_x" constraint.dofs = [constraint.dofs, [nodes(i); 4]];
case "rot_y" constraint.dofs = [constraint.dofs, [nodes(i); 5]];
case "rot_z" constraint.dofs = [constraint.dofs, [nodes(i); 6]];
case "warp" constraint.dofs = [constraint.dofs, [nodes(i); 7]];
case "~"
if (++i > ii)
error(["Ç äÝóìåõóç Ý÷åé DoFs ãéá ðåñéóóüôåñïõò êüìâïõò áðü ôïõò ", num2str(ii), " ðïõ äßíïíôáé"]);
endif
otherwise error(["ÂñÝèçêå ìç Ýãêõñï üíïìá âáèìïý åëåõèåñßáò: ", dof{1}]);
endswitch
endfor
if (isempty(constraint.dofs)) error("Ç äÝóìåõóç ðñÝðåé íá ðåñéëáìâÜíåé ôïõëÜ÷éóôïí Ýíá âáèìü åëåõèåñßáò"); endif
% Áí ïé DoFs äßíïíôáé ìüíï ìéá öïñÜ ãéá üëïõò ôïõò êüìâïõò, åðÝêôåéíå ôïõò
if (i == 1)
j = columns(constraint.dofs);
dofs = constraint.dofs;
for i = 2:ii
dofs(1, :) = nodes(i);
constraint.dofs = [constraint.dofs, dofs];
endfor
endif
% Öüñôùóç ôïõ ðßíáêá Ö (óõó÷åôßóåùò ôùí DoFs)
% Åßíáé óôï #text
if (~isempty(node.getFirstChild) && node.getFirstChild.getNodeType == 3) # TEXT_NODE
i = columns(constraint.dofs) + 1;
nums = str2num(node.getFirstChild.getNodeValue);
j = length(nums);
if (mod(j, i))
error(["Ãéá ", num2str(i - 1), " äåóìåõìÝíïõò êüìâïõò áíáìÝíåôáé ãéá ôïí ðßíáêá, ðëÞèïò óôïé÷åßùí ðïëëáðëÜóéï ôùí ", ...
num2str(i), ", âñÝèçêáí ", num2str(j)]);
endif
% Ï ðßíáêáò ó÷Ýóåùí ìåôáîý ôùí ìåôáêéíÞóåùí
constraint.disp_eq = reshape(nums, i, j / i)';
constraint.disp_const = constraint.disp_eq(:, i)';
constraint.disp_eq(:, i) = [];
endif
endfunction
% ËåêôéêÞ áíÜëõóç ìéáò ïìÜäáò áíôéêåéìÝíùí ôïõ xml, ð.÷. materials Þ nodes
% in: node: Ôï xml element ôçò ïìÜäáò ãéá ëåêôéêÞ áíÜëõóç
% in: name: Ôï üíïìá ðïõ ðñÝðåé íá Ý÷åé ôï xml element ôçò ïìÜäáò.
% Äåí ãßíåôáé Ýëåã÷ïò áí ôï node Ý÷åé áõôü ôï üíïìá.
% in: func: Ìéá óõíÜñôçóç åðåîåñãáóßáò ôùí ðáéäéêþí xml element ôïõ xml element
% ôçò ïìÜäáò
% error: ÓöÜëìá êáôÜ ôçí ëåêôéêÞ áíÜëõóç Þ ìç Ýãêõñá äåäïìÝíá.
function parseGroupOfNoCheck(node, name, func)
global data; % Ôá äåäïìÝíá ôïõ öïñÝá, üðùò Ý÷ïõí öïñôùèåß ìÝ÷ñé ôþñá.
child = node.getFirstElementChild;
data.(name) = {};
while ~isempty(child)
try
newIdx = length(data.(name)) + 1;
item.id = num2str(newIdx); % Áðïèçêåýåôáé ðñïóùñéíÜ ãéá ôï error handling
item = func(child);
% ¸ëåã÷ïò åãêõñüôçôáò id
if (length(item.id))
if (~isXmlName(item.id)) error(["Ìç Ýãêõñç óýíôáîç ãéá ôï @id=", item.id]); endif
data.map.(name).(item.id) = newIdx; % Êáôá÷þñçóç óå åõñåôÞñéï öéëéêþí ïíïìÜôùí
else
item.id = num2str(newIdx); % Áëëéþò ôï id åßíáé ï áýîùí áñéèìüò
endif
% Êáôá÷þñçóç óå âéâëéïèÞêç
data.(name){newIdx} = item;
child = child.getNextElementSibling;
catch err
err.message = ["Ðñüâëçìá óôç âéâëéïèÞêç ", name, ", óôï óôïé÷åßï ", item.id, "\n", err.message];
error(err);
end_try_catch
endwhile
endfunction
% ËåêôéêÞ áíÜëõóç ìéáò ïìÜäáò áíôéêåéìÝíùí ôïõ xml, ð.÷. materials Þ nodes
% in: node: Ôï xml element ôçò ïìÜäáò ãéá ëåêôéêÞ áíÜëõóç
% in: name: Ôï üíïìá ðïõ ðñÝðåé íá Ý÷åé ôï xml element ôçò ïìÜäáò.
% Áí äåí Ý÷åé áõôü ôï üíïìá åßíáé óöÜëìá.
% in: func: Ìéá óõíÜñôçóç åðåîåñãáóßáò ôùí ðáéäéêþí xml element ôïõ xml element
% ôçò ïìÜäáò
% error: ÓöÜëìá êáôÜ ôçí ëåêôéêÞ áíÜëõóç Þ ìç Ýãêõñá äåäïìÝíá.
function parseGroupOf(node, name, func)
parseCheckElementName(node, name);
parseGroupOfNoCheck(node, name, func);
endfunction
% ËåêôéêÞ áíÜëõóç ìéáò ïìÜäáò áíôéêåéìÝíùí ôïõ xml, ð.÷. materials Þ nodes
% in: node: Ôï xml element ôçò ïìÜäáò ãéá ëåêôéêÞ áíÜëõóç
% in: name: Ôï üíïìá ðïõ ðñÝðåé íá Ý÷åé ôï xml element ôçò ïìÜäáò.
% Áí äåí Ý÷åé áõôü ôï üíïìá äåí öïñôþíåôáé ôßðïôá.
% in: func: Ìéá óõíÜñôçóç åðåîåñãáóßáò ôùí ðáéäéêþí xml element ôïõ xml element
% ôçò ïìÜäáò
% out: parsed: true áí ç âéâëéïèÞêç õðÞñ÷å
% error: ÓöÜëìá êáôÜ ôçí ëåêôéêÞ áíÜëõóç Þ ìç Ýãêõñá äåäïìÝíá.
function parsed = parseGroupOfIfExist(node, name, func)
global data; % Ôá äåäïìÝíá ôïõ öïñÝá, üðùò Ý÷ïõí öïñôùèåß ìÝ÷ñé ôþñá.
if (~isempty(node) && strcmp(node.getNodeName, name))
parseGroupOfNoCheck(node, name, func);
parsed = true;
else data.(name) = {}; data.map.(name) = {}; parsed = false;
endif
endfunction
%{
function parsed = parseOutputOptionsIfExist(library)
global data; % Ôá äåäïìÝíá ôïõ öïñÝá, üðùò Ý÷ïõí öïñôùèåß ìÝ÷ñé ôþñá.
solverDefaultSettings();
if (~isempty(node) && strcmp(node.getNodeName, "output-options"))
child = node.getFirstElementChild;
% solver parsing
if (~isempty(child) && strcmp(child.getNodeName, "solver"))
b = child.getAttribute("tolerance");
a = str2num(b);
if (length(a))
if (length(a) ~= 1 || a < 10^-15 || a > 10^-2)
error(["Conjugent Gradient/Residuals tolerance ðñÝðåé íá åßíáé 10^-15 ùò 10^-2, âñÝèçêå ", b]);
endif
data.solver.settings.tolerance = a
endif
b = child.getAttribute("iterations");
a = uint32(str2num(b));
if (length(a))
if (length(a) ~= 1 || ~a)
error(["Conjugent Gradient/Residuals âÞìáôá ðñÝðåé íá åßíáé áðü 1 êáé ðÜíù, âñÝèçêå ", b]);
endif
data.solver.settings.iterations = a
endif
b = child.getAttribute("min-reaction");
a = str2num(b);
if (length(a))
if (length(a) ~= 1 || ~a)
error(["Conjugent Gradient/Residuals âÞìáôá ðñÝðåé íá åßíáé áðü 1 êáé ðÜíù, âñÝèçêå ", b]);
endif
data.solver.settings.minReaction = a
endif
data.solver.settings.minReaction = 0;
data.solver.settings.minDisplacement = 0;
child = child.getNextElementSibling;
endif
endif
endfunction
%}
% Öïñôþíåé ôï áñ÷åßï xml ôïõ öïñÝá
% in: xml: Ôï üíïìá áñ÷åßïõ ôïõ áñ÷åßïõ xml
% error: ÓöÜëìá êáôÜ ôçí ëåêôéêÞ áíÜëõóç Þ ìç Ýãêõñá äåäïìÝíá.
function parseXML(xml)
try
document = xmlread(xml);
structure = document.getDocumentElement;
parseCheckElementName(structure, "structure");
% material parsing
library = structure.getFirstElementChild;
if (parseGroupOfIfExist(library, "materials", @parseMaterial))
library = library.getNextElementSibling;
endif
% section parsing
if (parseGroupOfIfExist(library, "frame_sections", @parseFrameSection))
library = library.getNextElementSibling;
endif
% load parsing
parseGroupOf(library, "loads", @parseLoad);
library = library.getNextElementSibling;
% node parsing
parseGroupOf(library, "nodes", @parseNode);
library = library.getNextElementSibling;
% element parsing
parseGroupOf(library, "elements", @parseElement);
library = library.getNextElementSibling;
% restraint parsing
parseGroupOf(library, "restraints", @parseRestraint);
library = library.getNextElementSibling;
% constraint parsing
if (parseGroupOfIfExist(library, "constraints", @parseConstraint))
library = library.getNextElementSibling;
endif
%{
% output-options parsing
if (parseOutputOptionsIfExist(library))
library = library.getNextElementSibling;
endif
%}
catch err
err.message = ["Ðñüâëçìá êáôÜ ôçí öüñôùóç ôïõ áñ÷åßïõ xml\n", err.message];
error(err);
end_try_catch;
endfunction;
% =============================================================== PRE-PROCESSING
% Õðïëïãßæåé ôá ÷áñáêôçñéóôéêÜ G ôùí õëéêþí
function calcMaterialProperties()
global data;
for i = 1:length(data.materials)
if (isfield(data.materials{i}, "v"))
data.materials{i}.G = data.materials{i}.E / 2 / (1 + data.materials{i}.v);
endif
endfor
endfunction
% Õðïëïãßæåé ôá ÷áñáêôçñéóôéêÜ A, Iy, Iz, It, Cs äéáôïìÞò ôýðïõ Ï,
% þóôå íá ìç ÷ñåéÜæåôáé ðëÝïí ôï åßäïò äéáôïìÞò
% in,out: section: Ç äéáôïìÞ ðëáéóßïõ
function section = calcFrameSection_O_Properties(section)
section.A = section.diameter.^2 * pi / 4;
section.Iz = section.Iy = section.diameter.^4 * pi / 64;
if (length(section.A) == 2)
section.A = section.A(1) - section.A(2);
section.Iz = section.Iy = section.Iy(1) - section.Iy(2);
endif
section.It = section.Iz + section.Iy;
section.It_S = section.Cs = 0;
endfunction
% Õðïëïãßæåé ôá ÷áñáêôçñéóôéêÜ A, Iy, Iz, It, Cs ôùí äéáôïìþí,
% þóôå íá ìç ÷ñåéÜæåôáé ðëÝïí ôï åßäïò äéáôïìÞò
% in,out: section: Ç äéáôïìÞ ðëáéóßïõ
function calcFrameSectionsProperties()
global data;
for i = 1:length(data.frame_sections)
switch(data.frame_sections{i}.type)
case "O"
data.frame_sections{i} = calcFrameSection_O_Properties(data.frame_sections{i});
case "generic" % åßíáé üëá õðïëïãéóìÝíá
%TODO: ËïéðÝò äéáôïìÝò
endswitch
endfor
endfunction
% Óõìðëçñþíåé ôá åðéêüìâéá öïñôßá ôùí êüìâùí
function calcNodalLoads()
global data;
% Áðáñéèìåß Ýíáí Ýíáí üëïõò ôïõò êüìâïõò
for nodeidx = 1:length(data.nodes)
node = data.nodes{nodeidx};
% Áðáñßèìçóç ôùí åðéêüìâéùí öïñôßùí ôïõ êüìâïõ, áí õðÜñ÷ïõí
if (isfield(node, "loads"))
data.nodes{nodeidx}.nodalLoads = zeros(1,7);
for loadidx = node.loads
load = data.loads{loadidx};
% Áí åßíáé äýíáìç îåêéíÜåé áðü ôï âáèìü åëåõèåñßáò 1, ñïðÞ áðü ôïí 4
if (load.force) start = 1; else start = 4; endif
data.nodes{nodeidx}.nodalLoads(start:start+2) += load.coords;
endfor
endif
endfor
endfunction
% Áöáéñåß á÷ñåßáóôïõò âáèìïýò åëåõèåñßáò áðü Ýíá óôïé÷åßï
% - Áöáéñåß ôéò ìçäåíéêÝò ãñáììÝò/óôÞëåò áðü Ýíáí ðßíáêá äõóêáìøßáò óôïé÷åßïõ
% - Ðñïóáñìüæåé ôï ìçôñþï óôñïöþí óå áõôÞ ôçí ôñïðïðïßçóç
% - Ðñïóáñìüæåé ôá æåýãç node-DoF óå áõôÞ ôçí ôñïðïðïßçóç
% in, out: K: Ôï ìçôñþï äõóêáìøßáò ôïõ óôïé÷åßïõ
% in, out: lcs: Ôï ìçôñþï óôñïöþí ôïõ óôïé÷åßïõ
% in, out: dofs: Ôá æåýãç node-DoF
function [K, lcs, dofs] = compressStiffness(K, lcs, dofs)
for i = rows(K):-1:1
if (sum(abs(K(i, :))) < 256 * eps)
K(i,:) = []; % ÄéáãñáöÞ ãñáììÞò (ðÜåé ôï öïñôßï)
K(:,i) = []; % ÄéáãñáöÞ óôÞëçò (ðÜåé ç ìåôáôüðéóç)
lcs(:,i) = []; % ÄéáãñáöÞ óôÞëçò
dofs(:,i) = []; % ÄéáãñáöÞ óôÞëçò (ðÜåé ï âáèìüò åëåõèåñßáò)
endif
endfor
endfunction
% Ìå âÜóç ôá æåýãç node-DoF åíüò óôïé÷åßïõ, åíçìåñþíåé ôïõò áíôßóôïé÷ïõò êüìâïõò
% ãéá ôï ðïéïé DoFs ôïõò ÷ñçóéìïðïéïýíôáé áðü ôï óõãêåêñéìÝíï óôïé÷åßï.
% in: dofs: Ôá æåýãç node-DoF
function enableDoFsOnNodes(dofs)
global data;
for pair = dofs % Áèëéïôçôá! Ôï for êáíåé áðáñßèìçóç óôçëþí êáé ü÷é ãñáììþí
i = pair(1); % pair: [node index, dof index]
if (~isfield(data.nodes{i}, "dofs")) data.nodes{i}.dofs = zeros(1, 7); endif
data.nodes{i}.dofs(pair(2)) = true;
endfor
endfunction
% ÌåôáôñÝðåé ôá öïñôßá ôùí óôïé÷åßùí (åóùôåñéêÜ êáé êáôáíåìçìÝíá) óå åðéêüìâéá
% in: dofs: Ðßíáêáò ìå 1ç ãñáììÞ ôïõò êüìâïõò ôùí öïñôßùí êáé 2ç ãñáììÞ ôï âáèìü åëåõèåñßáò
% in: loads: Ôá åðéêüìâéá öïñôßá, ßóá óå áñéèìü ìå ôéò óôÞëåò ôïõ dofs
function convertElementLoadsToNodeLoads(dofs, loads)
global data;
for i = 1:columns(dofs)
dof = dofs(:, i);
if (~isfield(data.nodes{dof(1)}, 'nodalLoads')) data.nodes{dof(1)}.nodalLoads = zeros(1, 7); endif
data.nodes{dof(1)}.nodalLoads(dof(2)) += loads(i);
endfor
endfunction
% Êïéíüò êþäéêáò ñÜâäïõ êáé ãñáììéêïý åëáôçñßïõ
% Ðëçñïöïñßåò óôéò êëÞóåéò createBarStiffness(), createLinearSpringStiffness()
% in, out: element: Ôï óôïé÷åßï ôçò ñÜâäïõ
% in: dofRange: Ôï åýñïò ôùí âáèìþí åëåõèåñßáò ðïõ åðçñåÜæåé ôï óôïé÷åßï.
% 1:3 ãéá ìåôáöïñéêïýò âáèìïýò êáé 4:6 ãéá óôñïöéêïýò.
function element = createLinearSpringCommon(element, dofRange)
element.stiffnessGlobal = element.lcsMatrix' * element.stiffness * element.lcsMatrix;
% Lookup Table: ÊÜèå ãñáììÞ ôïõ ìçôñþïõ äõóêáìøßáò óå ðïéï æåýãïò êüìâïõ-DoF áíôéóôïé÷åß
% Åöáñìüæåôáé áõôü ôï áíáóôñïöï format, ãéáôß ç for áðáñéèìåß óôÞëåò(!) êáé ü÷é ãñáììÝò
element.dofs(1, 1:3) = element.nodes(1);
element.dofs(1, 4:6) = element.nodes(2);
element.dofs(2, 1:3) = element.dofs(2, 4:6) = dofRange;
% ¸ëåã÷ïò ìÞðùò óôï êáèïëéêü êÜðïéïé âáèìïß åëåõèåñßáò äåí ìáò áðáó÷ïëïýí
[element.stiffnessGlobal, element.lcsMatrix, element.dofs] = ...
compressStiffness(element.stiffnessGlobal, element.lcsMatrix, element.dofs);
% ÓôñïöÞ áñ÷éêþí P0 óôï êáèïëéêü
if (isfield(element, "initial_load"))
P = element.initial_load;
element.loads = [P, -P];
element.loadGlobal = element.loads * element.lcsMatrix;
endif
% ÅíçìÝñùóç ôùí êüìâùí ãéá ôï ðïéïé âáèìïß åëåõèåñßáò åíåñãïðïéïýíôáé áðü ôï óôïé÷åßï
enableDoFsOnNodes(element.dofs);
if (isfield(element, "loadGlobal"))
convertElementLoadsToNodeLoads(element.dofs, element.loadGlobal);
endif
endfunction
% Õðïëïãßæåé üëá ôá áðáéôïýìåíá óôïé÷åßá ôçò ñÜâäïõ óå ôïðéêü êáé êáèïëéêü óýóôçìá
% Õðïëïãßæåé ôï L, ôï ôïðéêü êáé êáèïëéêü K, ôï ôïðéêü êáé êáèïëéêü P0,
% ôï ôïðéêü óýóôçìá óõíôåôáãìÝíùí êáé ôï ìçôñþï óôñïöÞò.
% Åíôïðßæåé ðïéïõò âáèìïýò åëåõèåñßáò, ðïéþí êüìâùí, åìðëÝêåé óôï êáèïëéêü óýóôçìá
% êáé åíçìåñþíåé ôïõò êüìâïõò ãéá áõôïýò.
% in, out: element: Ôï óôïé÷åßï ôçò ñÜâäïõ
function element = createBarStiffness(element)
global data;
% ÁíÜêôçóç äåäïìÝíùí áðü ôá index ôïõò
material = data.materials{element.material};
section = data.frame_sections{element.section};
node1 = data.nodes{element.nodes(1)}.coords;
node2 = data.nodes{element.nodes(2)}.coords;
% Õðïëïãéóìüò óõóôÞìáôïò óõíôåôáãìÝíùí
element.L = norm(node2 - node1);
if (~element.L) error(["ÑÜâäïò ", element.id, ", ìçäåíéêïý ìÞêïõò"]); endif
element.direction = (node2 - node1) / element.L;
element.lcsMatrix = [element.direction 0 0 0; 0 0 0 element.direction];
% Õðïëïãéóìüò ìçôñþïõ äõóêáìøßáò
K = material.E * section.A / element.L;
element.stiffness = [K, -K; -K, K];
element = createLinearSpringCommon(element, 1:3);
endfunction
% Õðïëïãßæåé üëá ôá áðáéôïýìåíá óôïé÷åßá ôïõ ãñáììéêïý åëáôçñßïõ óå ôïðéêü êáé êáèïëéêü óýóôçìá
% Õðïëïãßæåé ôï ôïðéêü êáé êáèïëéêü K, ôï ôïðéêü êáé êáèïëéêü P0,
% ôï ôïðéêü óýóôçìá óõíôåôáãìÝíùí êáé ôï ìçôñþï óôñïöÞò.
% Åíôïðßæåé ðïéïõò âáèìïýò åëåõèåñßáò, ðïéþí êüìâùí, åìðëÝêåé óôï êáèïëéêü óýóôçìá
% êáé åíçìåñþíåé ôïõò êüìâïõò ãéá áõôïýò.
% in, out: element: Ôï óôïé÷åßï ôïõ åëáôçñßïõ
function element = createLinearSpringStiffness(element)
if (length(element.nodes) == 1)
% Õðïëïãéóìüò óõóôÞìáôïò óõíôåôáãìÝíùí
element.lcsMatrix = element.direction;
% Õðïëïãéóìüò ìçôñþïõ äõóêáìøßáò
element.stiffness = element.K;
element.stiffnessGlobal = element.lcsMatrix' * element.stiffness * element.lcsMatrix;
% Lookup Table: ÊÜèå ãñáììÞ ôïõ ìçôñþïõ äõóêáìøßáò óå ðïéï æåýãïò êüìâïõ-DoF áíôéóôïé÷åß
% Åöáñìüæåôáé áõôü ôï áíáóôñïöï format, ãéáôß ç for áðáñéèìåß óôÞëåò(!) êáé ü÷é ãñáììÝò
element.dofs(1, 1:3) = element.nodes(1);
element.dofs(2, 1:3) = 1:3;
% ¸ëåã÷ïò ìÞðùò óôï êáèïëéêü êÜðïéïé âáèìïß åëåõèåñßáò äåí ìáò áðáó÷ïëïýí
[element.stiffnessGlobal, element.lcsMatrix, element.dofs] = ...
compressStiffness(element.stiffnessGlobal, element.lcsMatrix, element.dofs);
% ÓôñïöÞ áñ÷éêþí P0 óôï êáèïëéêü
if (isfield(element, "initial_load"))
element.loads = element.initial_load;
element.loadGlobal = element.loads * element.lcsMatrix;
endif
% ÅíçìÝñùóç ôùí êüìâùí ãéá ôï ðïéïé âáèìïß åëåõèåñßáò åíåñãïðïéïýíôáé áðü ôï óôïé÷åßï
enableDoFsOnNodes(element.dofs);
if (isfield(element, "loadGlobal"))
convertElementLoadsToNodeLoads(element.dofs, element.loadGlobal);
endif
else
% Õðïëïãéóìüò óõóôÞìáôïò óõíôåôáãìÝíùí
element.lcsMatrix = [element.direction 0 0 0; 0 0 0 element.direction];
% Õðïëïãéóìüò ìçôñþïõ äõóêáìøßáò
element.stiffness = [element.K, -element.K; -element.K, element.K];
element = createLinearSpringCommon(element, 1:3);
endif
endfunction
% Õðïëïãßæåé üëá ôá áðáéôïýìåíá óôïé÷åßá ôïõ óôñïöéêïý åëáôçñßïõ óå ôïðéêü êáé êáèïëéêü óýóôçìá
% Õðïëïãßæåé ôï ôïðéêü êáé êáèïëéêü K, ôï ôïðéêü êáé êáèïëéêü P0,
% ôï ôïðéêü óýóôçìá óõíôåôáãìÝíùí êáé ôï ìçôñþï óôñïöÞò.
% Åíôïðßæåé ðïéïõò âáèìïýò åëåõèåñßáò, ðïéþí êüìâùí, åìðëÝêåé óôï êáèïëéêü óýóôçìá
% êáé åíçìåñþíåé ôïõò êüìâïõò ãéá áõôïýò.
% in, out: element: Ôï óôïé÷åßï ôïõ åëáôçñßïõ
function element = createTorsionSpringStiffness(element)
if (length(element.nodes) == 1)
% Õðïëïãéóìüò óõóôÞìáôïò óõíôåôáãìÝíùí
element.lcsMatrix = element.direction;
% Õðïëïãéóìüò ìçôñþïõ äõóêáìøßáò
element.stiffness = element.K;
element.stiffnessGlobal = element.lcsMatrix' * element.stiffness * element.lcsMatrix;
% Lookup Table: ÊÜèå ãñáììÞ ôïõ ìçôñþïõ äõóêáìøßáò óå ðïéï æåýãïò êüìâïõ-DoF áíôéóôïé÷åß
% Åöáñìüæåôáé áõôü ôï áíáóôñïöï format, ãéáôß ç for áðáñéèìåß óôÞëåò(!) êáé ü÷é ãñáììÝò
element.dofs(1, 1:3) = element.nodes(1);
element.dofs(2, 1:3) = 4:6;
% ¸ëåã÷ïò ìÞðùò óôï êáèïëéêü êÜðïéïé âáèìïß åëåõèåñßáò äåí ìáò áðáó÷ïëïýí
[element.stiffnessGlobal, element.lcsMatrix, element.dofs] = ...
compressStiffness(element.stiffnessGlobal, element.lcsMatrix, element.dofs);
% ÓôñïöÞ áñ÷éêþí P0 óôï êáèïëéêü
if (isfield(element, "initial_load"))
element.loads = element.initial_load;
element.loadGlobal = element.loads * element.lcsMatrix;
endif
% ÅíçìÝñùóç ôùí êüìâùí ãéá ôï ðïéïé âáèìïß åëåõèåñßáò åíåñãïðïéïýíôáé áðü ôï óôïé÷åßï
enableDoFsOnNodes(element.dofs);
if (isfield(element, "loadGlobal"))
convertElementLoadsToNodeLoads(element.dofs, element.loadGlobal);
endif
else
% Õðïëïãéóìüò óõóôÞìáôïò óõíôåôáãìÝíùí
element.lcsMatrix = [element.direction 0 0 0; 0 0 0 element.direction];
% Õðïëïãéóìüò ìçôñþïõ äõóêáìøßáò
element.stiffness = [element.K, -element.K; -element.K, element.K];
element = createLinearSpringCommon(element, 4:6);
endif
endfunction
% Õðïëïãßæåé üëá ôá áðáéôïýìåíá óôïé÷åßá ôçò äïêïý óå ôïðéêü êáé êáèïëéêü óýóôçìá
% Õðïëïãßæåé ôï L, ôï ôïðéêü êáé êáèïëéêü K, ôï ôïðéêü êáé êáèïëéêü P0,
% ôï ôïðéêü óýóôçìá óõíôåôáãìÝíùí êáé ôï ìçôñþï óôñïöÞò.
% Åíôïðßæåé ðïéïõò âáèìïýò åëåõèåñßáò, ðïéþí êüìâùí, åìðëÝêåé óôï êáèïëéêü óýóôçìá
% êáé åíçìåñþíåé ôïõò êüìâïõò ãéá áõôïýò.
% in, out: element: Ôï óôïé÷åßï ôçò ñÜâäïõ
function element = createBeamStiffness(element)
global data;
% ÁíÜêôçóç äåäïìÝíùí áðü ôá index ôïõò
material = data.materials{element.material};
section = data.frame_sections{element.section};
node1 = data.nodes{element.nodes(1)}.coords;
node2 = data.nodes{element.nodes(2)}.coords;
% Õðïëïãéóìüò óõóôÞìáôïò óõíôåôáãìÝíùí
L = element.L = norm(node2 - node1);
if (~element.L) error(["Äïêüò ", element.id, ", ìçäåíéêïý ìÞêïõò"]); endif
axisX = (node2 - node1) / element.L;
if (isfield(element, "axisZ")) % åßíáé ìïíáäéáßï
axisZ = element.axisZ;
element = rmfield(element, "axisZ");
axisY = cross(axisZ, axisX);
n = norm(axisY);
if (n < 0.02)
error(["Óôï äïêü ", element.id, ", ï Üîïíáò z ðñÝðåé íá Ý÷åé ãùíßá ôïõëÜ÷éóôïí 1.145° ìå ôïí Üîïíá x, Ý÷åé ", ...
num2str(asin(n * 180 / pi)), "°"]);
endif
axisY /= n;
axisZ = cross(axisX, axisY);
element.lcs = [axisX; axisY; axisZ];
else
axisZ = [0 0 1];
n = dot(axisX, axisZ);
if (abs(n) > 0.9998)
axisZ = -sign(n) * [1 0 0];
endif
axisY = cross(axisZ, axisX);
axisY /= norm(axisY);
axisZ = cross(axisX, axisY);
element.lcs = [axisX; axisY; axisZ];
endif
% ÓôñÝâëùóç, óôñïöÝò êáé ìåôáêéíÞóåéò
element.lcsMatrix(14, 14) = element.lcsMatrix(7, 7) = 1;
element.lcsMatrix(1:3, 1:3) = element.lcsMatrix(4:6, 4:6) = ...
element.lcsMatrix(8:10, 8:10) = element.lcsMatrix(11:13, 11:13) = element.lcs;
%
% Õðïëïãéóìüò óõíïëéêïý êáôáíåìçìÝíïõ öïñôßïõ
if (isfield(element, 'distributed_loads'))