Academic Journal of Engineering and Technology Science, 2024, 7(4); doi: 10.25236/AJETS.2024.070417.
Mingkun Guo, Zhuoyi Yang, Huadong Shao
Naval Architecture and Port Engineering College, Shandong Jiaotong University, Weihai, China
Dynamics performance is a crucial mechanical performance indicator for stiffened plates. Therefore, this paper investigates the topology optimization design for minimizing dynamic compliance of stiffened plates under time-domain loads. Based on the SIMP (Simple isotropic material with penalization), an interpolation model for stiffened plates is established. To enhance the accuracy of sensitivity calculations, a sensitivity analysis strategy that discretizes before differentiating is employed. By introducing adjoint variables, the cost of computing the gradient of the function is made linearly dependent on the number of state variables, significantly improving computational efficiency. With the constraint of the stiffener volume fraction, the topology optimization problem for minimizing dynamic compliance of stiffened plates under half-wave sinusoidal loads is solved. Finally, through a comparison of numerical results from example cases with the dynamic response of traditional unidirectional stiffened plates, it is found that the maximum displacement of the optimized stiffened plate is approximately 30.5% of the maximum displacement of the unidirectional stiffened plate. This verifies that the optimized stiffened plate exhibits superior dynamics performance.
Time-domain load, Topology optimization, Dynamic compliance, Adjoint variable method
Mingkun Guo, Zhuoyi Yang, Huadong Shao. Dynamics Topology Optimization of Stiffened Plates under Time-Domain Dynamic Loads. Academic Journal of Engineering and Technology Science (2024) Vol. 7, Issue 4: 114-121. https://doi.org/10.25236/AJETS.2024.070417.
[1] Bedair O. Analysis and limit state design of stiffened plates and shells: a world view [J]. Applied Mechanics Reviews, 2009, 62(2):020-801.
[2] Quinn D, Murphy A, McEwan W, et al. Non-prismatic sub-stiffening for stiffened panel plates—Stability behaviour and performance gains[J]. Thin-Walled Structures, 2010, 48(6): 401-413.
[3] Xu M C, Song Z J, Zhang B W, et al. Empirical formula for predicting ultimate strength of stiffened panel of ship structure under combined longitudinal compression and lateral loads [J]. Ocean Engineering, 2018, 162: 161-175.
[4] Goel M D, Matsagar V A, Gupta A K. Dynamic response of stiffened plates under air blast[J]. International Journal of Protective Structures, 2011, 2(1): 139-155.
[5] Yang Y, Li J J, Zhang Y, et al. A semi-analytical analysis of strength and critical buckling behavior of underwater ring-stiffened cylindrical shells[J]. Engineering Structures, 2021, 227: 111396.
[6] Quinn D, Murphy A, McEwan W, et al. Stiffened panel stability behaviour and performance gains with plate prismatic sub-stiffening[J]. Thin-Walled Structures, 2009, 47(12): 1457-1468.
[7] Omidali M, Khedmati M R. Reliability-based design of stiffened plates in ship structures subject to wheel patch loading[J]. Thin-Walled Structures, 2018, 127: 416-424.
[8] Yang B, Wu J, Soares C G, et al. Dynamic ultimate strength of outer bottom stiffened plates under in-plane compression and lateral pressure[J]. Ocean Engineering, 2018, 157: 44-53.
[9] Amaral R R, Troina G S, Fragassa C, et al. Constructal design method dealing with stiffened plates and symmetry boundaries[J]. Theoretical and Applied Mechanics Letters, 2020, 10(5): 366-376.
[10] Li B, Hong J, Wang Z, et al. An innovative layout design methodology for stiffened plate/shell structures by material increasing criterion[J]. Journal of engineering materials and technology, 2013, 135(2): 021012.
[11] Lima J P S, Cunha M L, dos Santos E D, et al. Constructal Design for the ultimate buckling stress improvement of stiffened plates submitted to uniaxial compressive load[J]. Engineering Structures, 2020, 203: 109883.
[12] Farkas J, Jármai K, Snyman J A. Global minimum cost design of a welded square stiffened plate supported at four corners[J]. Structural and Multidisciplinary Optimization, 2010, 40: 477-489.
[13] Snyman J A, Fatti L P. A multi-start global minimization algorithm with dynamic search trajectories [J]. Journal of optimization theory and applications, 1987, 54: 121-141.
[14] Soares C G, Gordo J M. Design methods for stiffened plates under predominantly uniaxial compression [J]. Marine Structures, 1997, 10(6): 465-497.
[15] Zhao X, Wu B, Li Z, et al. A method for topology optimization of structures under harmonic excitations [J]. Structural and Multidisciplinary Optimization, 2018, 58: 475-487.
[16] Sasikumar K S K, Arulshri K P, Selvakumar S. Optimization of constrained layer damping parameters in beam using taguchi method[J]. Iranian Journal of Science and Technology, Transactions of Mechanical Engineering, 2017, 41: 243-250.
[17] Ma X, Wang F, Aage N, et al. Generative design of stiffened plates based on homogenization method[J]. Structural and Multidisciplinary Optimization, 2021, 64: 3951-3969.
[18] Zhou M, Rozvany G I N. The COC algorithm, Part II: Topological, geometrical and generalized shape optimization [J]. Computer methods in applied mechanics and engineering, 1991, 89(1-3): 309-336.
[19] Wang F, Lazarov B S, Sigmund O. On projection methods, convergence and robust formulations in topology optimization [J]. Structural and multidisciplinary optimization, 2011, 43: 767-784.