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Truss structure design using a length-oriented surface remeshing technique
1. | Department of Mathematics and Descriptive Geometry, Faculty of Civil Engineering, Slovak University of Technology, Radlinského 11, 81368 Bratislava, Slovak Republic, Slovak Republic |
2. | Hutnícka 10/51, 05201 Spišská Nová Ves, Slovak Republic |
References:
[1] |
M. R. Barnes, Form finding and analysis of tension structures by dynamic relaxation, International Journal of Space Structures, 14 (1999), 89-104.
doi: 10.1260/0266351991494722. |
[2] |
K. U. Bletzinger, M. Firl, J. Linhard and R. Wüchner, Optimal shapes of mechanically motivated surfaces, Computer Methods in Applied Mechanics and Engineering, 199 (2010), 324-333.
doi: 10.1016/j.cma.2008.09.009. |
[3] |
M. Húska, M. Medĭa, K. Mikula, P. Novysedlák and M. Remeší ková, A new form-finding method based on mean curvature flow of surfaces, Proceedings of ALGORITMY 2012, 19th Conference on Scientific Computing, Podbanské, Slovakia, September 9-14, 2012, Publishing House of STU, (2012), 120-131. |
[4] |
M. Meyer, M. Desbrun, P. Schroeder and A. H. Barr, Discrete differential geometry operators for triangulated 2-manifolds, Visualization and Mathematics III (Hans-Christian Hege and Konrad Polthier, eds.), 3 (2003), 35-57. |
[5] |
B. Maurin and R. Motro, The surface stress density method as a form-finding tool for tensile membranes, Engineering Structures, 20 (1998), 712-719.
doi: 10.1016/S0141-0296(97)00108-9. |
[6] |
K. Mikula, M. Remeší ková, P. Sarkoci, D. Ševčovič, Surface evolution with tangential redistribution of points, to appear in SIAM Journal of Scientific Computing. |
[7] |
K. Mikula and D. Ševčovič, Evolution of plane curves driven by a nonlinear function of curvature and anisotropy, SIAM Journal on Applied Mathematics, 61 (2001), 1473-1501.
doi: 10.1137/S0036139999359288. |
[8] |
K. Mikula and D. Ševčovič, A direct method for solving an anisotropic mean curvature flow of planar curve with an external force, Mathematical Methods in Applied Sciences, 27 (2004), 1545-1565.
doi: 10.1002/mma.514. |
[9] |
K. Mikula and J. Urbán, 3D curve evolution algorithm with tangential redistribution for a fully automatic finding of an ideal camera path in virtual colonoscopy, Scale Space and Variational Methods in Computer Vision, Lecture Notes in Computer Science, 6667 (2012), 640-652.
doi: 10.1007/978-3-642-24785-9_54. |
[10] |
A. Mottaghi Rad, H. Jamili and S. A. Behnejad, Length equalization of elements in single layer lattice spatial structures, Abstract Book of the IASS-APCS 2012 Conference, Seoul, Korea, (2012), 266-273. |
[11] |
J. C. C. Nitsche, A new uniqueness theorem for minimal surfaces, Arch. Rat. Mech. Anal., 52 (1973), 319-329.
doi: 10.1007/BF00247466. |
[12] |
F. Pantano and H. Tamai, Geometric Multi-objective Optimization of Free-form Grid Shell Structures, Abstract Book of the IASS-APCS 2012 Conference, Seoul, Korea, (2012), 85-93. |
[13] |
R. M. O. Pauletti and P. M. Pimenta, The natural force density method for the shape finding of taut structures, Computer Methods in Applied Mechanics and Engineering, 197 (2008), 4419-4428.
doi: 10.1016/j.cma.2008.05.017. |
[14] |
U. Pinkall and K. Polthier, Computing discrete minimal surfaces and their conjugates, Experim. Math., 2 (1993), 15-36.
doi: 10.1080/10586458.1993.10504266. |
[15] |
H. J. Scheck, The force density method for form finding and computation of general networks, Computer Methods in Applied Mechanics and Engineering, 3 (1974), 115-134.
doi: 10.1016/0045-7825(74)90045-0. |
[16] |
B. H. V. Topping and P. Ivanyi, Computer Aided Design of Cable Membrane Structures, Saxe-Coburg Publications on Computational Engineering, 2008. |
show all references
References:
[1] |
M. R. Barnes, Form finding and analysis of tension structures by dynamic relaxation, International Journal of Space Structures, 14 (1999), 89-104.
doi: 10.1260/0266351991494722. |
[2] |
K. U. Bletzinger, M. Firl, J. Linhard and R. Wüchner, Optimal shapes of mechanically motivated surfaces, Computer Methods in Applied Mechanics and Engineering, 199 (2010), 324-333.
doi: 10.1016/j.cma.2008.09.009. |
[3] |
M. Húska, M. Medĭa, K. Mikula, P. Novysedlák and M. Remeší ková, A new form-finding method based on mean curvature flow of surfaces, Proceedings of ALGORITMY 2012, 19th Conference on Scientific Computing, Podbanské, Slovakia, September 9-14, 2012, Publishing House of STU, (2012), 120-131. |
[4] |
M. Meyer, M. Desbrun, P. Schroeder and A. H. Barr, Discrete differential geometry operators for triangulated 2-manifolds, Visualization and Mathematics III (Hans-Christian Hege and Konrad Polthier, eds.), 3 (2003), 35-57. |
[5] |
B. Maurin and R. Motro, The surface stress density method as a form-finding tool for tensile membranes, Engineering Structures, 20 (1998), 712-719.
doi: 10.1016/S0141-0296(97)00108-9. |
[6] |
K. Mikula, M. Remeší ková, P. Sarkoci, D. Ševčovič, Surface evolution with tangential redistribution of points, to appear in SIAM Journal of Scientific Computing. |
[7] |
K. Mikula and D. Ševčovič, Evolution of plane curves driven by a nonlinear function of curvature and anisotropy, SIAM Journal on Applied Mathematics, 61 (2001), 1473-1501.
doi: 10.1137/S0036139999359288. |
[8] |
K. Mikula and D. Ševčovič, A direct method for solving an anisotropic mean curvature flow of planar curve with an external force, Mathematical Methods in Applied Sciences, 27 (2004), 1545-1565.
doi: 10.1002/mma.514. |
[9] |
K. Mikula and J. Urbán, 3D curve evolution algorithm with tangential redistribution for a fully automatic finding of an ideal camera path in virtual colonoscopy, Scale Space and Variational Methods in Computer Vision, Lecture Notes in Computer Science, 6667 (2012), 640-652.
doi: 10.1007/978-3-642-24785-9_54. |
[10] |
A. Mottaghi Rad, H. Jamili and S. A. Behnejad, Length equalization of elements in single layer lattice spatial structures, Abstract Book of the IASS-APCS 2012 Conference, Seoul, Korea, (2012), 266-273. |
[11] |
J. C. C. Nitsche, A new uniqueness theorem for minimal surfaces, Arch. Rat. Mech. Anal., 52 (1973), 319-329.
doi: 10.1007/BF00247466. |
[12] |
F. Pantano and H. Tamai, Geometric Multi-objective Optimization of Free-form Grid Shell Structures, Abstract Book of the IASS-APCS 2012 Conference, Seoul, Korea, (2012), 85-93. |
[13] |
R. M. O. Pauletti and P. M. Pimenta, The natural force density method for the shape finding of taut structures, Computer Methods in Applied Mechanics and Engineering, 197 (2008), 4419-4428.
doi: 10.1016/j.cma.2008.05.017. |
[14] |
U. Pinkall and K. Polthier, Computing discrete minimal surfaces and their conjugates, Experim. Math., 2 (1993), 15-36.
doi: 10.1080/10586458.1993.10504266. |
[15] |
H. J. Scheck, The force density method for form finding and computation of general networks, Computer Methods in Applied Mechanics and Engineering, 3 (1974), 115-134.
doi: 10.1016/0045-7825(74)90045-0. |
[16] |
B. H. V. Topping and P. Ivanyi, Computer Aided Design of Cable Membrane Structures, Saxe-Coburg Publications on Computational Engineering, 2008. |
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