The Vth Generation of The INDUCTION DESIGN

ALGODesign 
KeiRiki1 : 
Use
of the program:
“KeiRiki1w”
may be downloaded from this site and used free of charge. However, the
creation of derivative works, commercial use, and so on are prohibited
without the express written consent of the author. When
you release or publish the result ( ; design, research, thesis, program,
etc.) achieved by using this program or referring to this program, it is
necessary to describe clearly about it indicating the name of this program
and the authors.
This
program is intended for educational purposes only. Questions
regarding use of program will not be answered.
Constructive suggestions and opinions will be accepted,
but may not be answered.
“KeiRiki1w” is an open version of “KeiRiki1”,
which was actually used in the design of “ShinMinamataMon”. It shares
almost all of the functionality of the original version.
For other information about the program, please refer to
the README file.
KeiRiki program family:
“KeiRiki1”: The program used in the design of
“ShinMinamataMon”
“KeiRiki1w”: The open version made available on
this site.
The author: Makoto
Sei Watanabe, Makoto Ohsaki, Takashi Chiba
DISCLAIMER:
“KEIRIKI1W”
(THE PROGRAM) IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO FITNESS FOR A PARTICULAR
PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY
CLAIM, DAMAGES OR OTHER LIABILITY ARISING FROM, OUT OF OR IN CONNECTION WITH
THE PROGRAM OR THE USE OF THE PROGRAM.
“KEIRIKI2” (THE PROGRAM) IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY ARISING FROM, OUT OF OR IN CONNECTION WITH THE PROGRAM OR THE USE OF THE PROGRAM.
Download "KeiRiki2" ：800KB
Download "KeiRiki1w" ：900KB

Descriptions of parameters and algorithms: (about
KeiRiki1w)
General description ‘KeiRiki1w’ generates a meshtype
optimal structure for a given curved surface or a plane under specified
growing rule.
Outline
of generating process
1. Specify the type of the surface.
2. Generate a mesh under specified condition.
3. Assign nodal loads.
4. Select a list of members.
5. Carry out structural optimization.
Technical
terms
Shape : curved
surface or a plane; arbitrary given under some restriction.
Node
: a point located on the surface.
Member : a segment of a
line between two nodes.
Branching : the state where two members
grow from a node.
Evaded region : a region where no node or member can exist; arbitrary given.
Part A Shape Generating Program
1 Input variables
All the variables can be set by KeiRiki1w.
1.
I_{ran} Initial seed for random variables (arbitrary natural number). The shape can
be controlled by modifying I_{ran}.
2.
N_{pmax} Upper bound for for the number of nodes N_{p} (less than
4000). Since branching is done simultaneously at all the front nodes, the
generating process terminates if N_{p} exceeds N_{pmax}.
Also N_{p} might be reduced by the postprocess of deleting
unnecessary members.
3. N_{fp} Number of initial front nodes at the lowest boundary.
4. X_{fp }Locations of the initial front nodes. Number of nodes is N_{fp} and 0< X_{fp}<1.
5.
L_{0} Standard length of members (preferably between 0.1 and 0.2).
6.
ΔL
Ratio of standard deviation of member length to L_{0} (preferably
about 0.2).
7. θ Standard value of branching angle (preferably between 20 and 30 degrees).
8.
Δθ Ratio of standard deviation of branching angleθ (preferably about 0.2).
9. L_{min} Minimum value of member length (preferably between 0.1 and
0.2). 10. θ_{min} Minimum value of branching angle (preferably between 0.1 and 0.2). If the
angle is less than θ_{min}, one of the branching members is to be
removed and the nodes generated by the members are combined.
11. S_{type }Surface type
12. R_{x}, R_{y} Center of evading region
13. R_{r} Radius of evading region
2 Algorithm
First generate the shape on the normalized
plane (0<x<1, 0<y<3), and map it on the surface or cube.
1. Assign N_{fp} front nodes on the lowest boundary. The coordinates
are denoted by (X_{i},Y_{i})，(I=1,2,…,N_{fp}),
where the two endpoints of the lowest boundary are (0,0) and (1,0).
2. Let the initial direction be θ_{i}=(0,1), (I=1,2,…,N_{fp}).
3. Generate branches (k=1,2) at all the front nodes as follows:
1) Generate uniform random number r between 0 and 1, and define the member
length L_{k} by 2) Generate uniform random number r, and define the member directionθ_{k}(k=1,2)
by 3) Locate a new node by moving from node i in the direction of θ_{k} , and add a member to connect node I and the new node.
4) If the member intersects with the boundary of the evaded region where no
node or member can exist, add a new node at the intersection.
5) If the member intersects with an existing member, connect the node i with
one of the end node of the existing member that is farther than node i.
Hence, the member is added without increasing the number of nodes.
6) Let the new nodes be front nodes, where the generating directions are
defined by the directions of the new members.
4. Update the lists of members and nodes.
5. Go to 3 if the number of nodes is less than N_{pmax}.
6. Carry out the following process until no short member of
narrow branching
angle exists.
1) Combine the two end nodes of the member whose length is less than L_{0 *}L_{min}.
2) Delete the shorter member of a branch whose angle is less than θ_{0}*θ_{min}.
3) Remove the floating nodes.
Part B Apti/Opti mizing Program
1 Input variables (opt.dat)
The variable that is NOT indicated by `INPUT
FROM KeiRiki1w’ should be modified by directly editing `opt.dat.’
1. E, ν, ρ Elastic modulus, Poisson’s ratio, Weight density (Default
values for steel are given)
2. h Thickness of member; indicates the thickness of flange if N_{plate} =2. (INPUT FROM KeiRiki1w)
3. σ_{b} Upperbound stress (Increase (decrease) if the optimal members are too thin
(thick); standard value of steel is given)
4. S_{x}, S_{y}, S_{z} Scale parameter for x , y,
zdirections. (INPUT FROM KeiRiki1w)
5.
N_{cs }Number of member widths given in `dv.dat’. (INPUT FROM
KeiRiki1w)
6. S_{type }Type of surface (1: Bezier or twisted Bezier, 0: Cube; DO
NOT MODIFY).
7. N_{max} Number of maximum iterations (Decrease if computational
time is too much.)
8. D_{max} Maximum ratio of the occupied area to the total surface
area (Decrease if computational
time is too much.)
9. IC Level of correction after optimization (0: none, 1: low, 2:high; DO NOT
MODIFY)
10. Is Scaling parameter (1: automatic, 0: manual) (INPUT FROM
KeiRiki1w)
11.
N_{plate} Number of flanges (1: single, 2: double) . Disabled if
Is=1. (INPUT FROM KeiRiki1w)
12. Dplate Distance between flanges (1: single, 2: double) . Disabled if Is=1
or N_{plate} =1. (INPUT FROM KeiRiki1w)
2 dv.dat
Set by KeiRiki1w.
List
of member widths Wi (i=1,2, …, N_{cs}) for ranks 1,2, …, N_{cs}.
Increase
Wi (i=2, …, N_{cs}) if computation time for optimization is too
large.
Increase
(decrease) Wi (i=2, …, N_{cs}) if there exist too many members
with largest (smallest) rank in the optimal solution.
DO
NOT MODIFY W_{1}.
3 Load.dat
Set by KeiRiki1w.
1. N_{load} Number of loading sets.
2. I_{load} Set number.
3. J_{min}, J_{max} Lower and upper bounds of nodes to be
loaded by this set.
4. P_{x}, P_{y}, P_{z} Load vector.
Numerical output data
1. At
iterative steps of optimization: (result.dat) 2. After
optimization: (violate.dat)
A heuristic optimization method called `greedy method’ is used. : Wind load Apply 3.372 kN per m2 of member area in the ydirection, which is computer from the Japanese building code. The loads are applied at the only vertical plane for a cube; the loads are given at all the nodes for a Bezier surface. : Selfweight The selfweight of a member computed from the volume and weight density is applied in the vertical direction. The allowable stress is defined along with the Japanese code for steel structures. The stresses are computed at all the four corners of each member to find maximum absolute value of stress that is divided by the allowable stress to obtain the stress ratio. Two load cases in positive and negative ydirections are considered for wind loads. 4. Let J denote the set of members that has a rank below the maximum value. 5. Terminate the process if the number of iterative steps exceeds Nmax or the ratio of the occupied area to the surface area reaches Dmax; otherwise go to Step 2.
5
Apti/Opti mization algorithm (decreasing process)
Iteratively remove a floating member, and a
cantilevertype member if no additional load is applied at the end of the
cantilever.
General
Specifications
Units： `m’ for length, `kN’ for force.
The nodes at the ground level are
automatically fixed as supports.
