Nonlinear Analysis of Corrugated Core Sandwich Plates Using the Element-Free Galerkin Method
Abstract
1. Introduction
2. The Mesh-Free Galerkin Method
3. Determination of Elastic Constants of the Corrugated Cores
- <1>.
- Sinusoidally corrugated core
- <2>.
- Trapezoidal corrugated core
4. Meshless Control Equations for Geometric Nonlinearities in Corrugated Sandwich Plates
4.1. Displacement Field Function
4.2. Plate Stress and Strain
4.2.1. Linear Strain
4.2.2. Nonlinear Strain
4.3. Nonlinear Equilibrium Equations for Corrugated Plates
4.4. Boundary Conditions and Displacement Coordination Conditions
4.4.1. Full Transformation Method
4.4.2. Treatment of Boundary Conditions
5. Results and Discussion
5.1. Validation Studies
5.2. Four-Side Fixed Support Corrugated Sandwich Plate
5.3. Four-Side Simply Supported Corrugated Sandwich Plates
6. Conclusions
- (1)
- The proposed meshless model achieves high accuracy while requiring significantly fewer computational nodes compared to traditional finite element methods (FEMs) with fine mesh discretization;
- (2)
- The close agreement between the meshless and FEM solutions confirms the effectiveness and reliability of the proposed approach;
- (3)
- The method exhibits high computational efficiency and is well suited for numerical implementation, making it a promising tool for analyzing the nonlinear behavior of corrugated sandwich plate structures.
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
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P (Pa) | EFG Linear Solution (w/m) | ANSYS Linear Solution (w/m) | EFG Nonlinear Solution (w/m) | ANSYS Nonlinear Solution (w/m) | Relative Error of Linear Solution (%) | Relative Error of Nonlinear Solution (%) |
---|---|---|---|---|---|---|
50 | 0.012669 | 0.012892 | 0.01069 | 0.011193 | −1.73363 | −4.49031 |
100 | 0.025337 | 0.025785 | 0.017106 | 0.018208 | −1.73744 | −6.05064 |
150 | 0.038006 | 0.038667 | 0.021497 | 0.023068 | −1.71076 | −6.81203 |
200 | 0.050674 | 0.05157 | 0.024836 | 0.026829 | −1.73744 | −7.43002 |
250 | 0.063343 | 0.064462 | 0.027727 | 0.029931 | −1.73668 | −7.36461 |
P (Pa) | EFG Linear Solution (w/m) | ANSYS Linear Solution (w/m) | EFG Nonlinear Solution (w/m) | ANSYS Nonlinear Solution (w/m) | Relative Error of Linear Solution (%) | Relative Error of Nonlinear Solution (%) |
---|---|---|---|---|---|---|
50 | 0.012669 | 0.012858 | 0.01069 | 0.010883 | −1.47379 | −1.76973 |
100 | 0.025337 | 0.025717 | 0.017106 | 0.01745 | −1.47762 | −1.96963 |
150 | 0.038006 | 0.038575 | 0.021497 | 0.021934 | −1.47634 | −1.99416 |
200 | 0.050674 | 0.051435 | 0.024836 | 0.025375 | −1.47954 | −2.12571 |
250 | 0.063343 | 0.064294 | 0.027727 | 0.028195 | −1.47992 | −1.66093 |
P (Pa) | EFG Linear Solution (w/m) | ANSYS Linear Solution (w/m) | EFG Nonlinear Solution (w/m) | ANSYS Nonlinear Solution (w/m) | Relative Error of Linear Solution (%) | Relative Error of Nonlinear Solution (%) |
---|---|---|---|---|---|---|
50 | 0.011952 | 0.012201 | 0.010213 | 0.010786 | −2.04409 | −5.30873 |
100 | 0.023903 | 0.024402 | 0.016484 | 0.01781 | −2.0445 | −7.44357 |
150 | 0.035855 | 0.036604 | 0.020795 | 0.02273 | −2.04704 | −8.5143 |
200 | 0.047806 | 0.048805 | 0.024134 | 0.026546 | −2.04631 | −9.08649 |
250 | 0.059758 | 0.061001 | 0.026593 | 0.029696 | −2.03736 | −10.4482 |
P (Pa) | EFG Linear Solution (w/m) | ANSYS Linear Solution (w/m) | EFG Nonlinear Solution (w/m) | ANSYS Nonlinear Solution (w/m) | Relative Error of Linear Solution (%) | Relative Error of Nonlinear Solution (%) |
---|---|---|---|---|---|---|
50 | 0.012669 | 0.012858 | 0.01069 | 0.010883 | −1.47379 | −1.76973 |
100 | 0.025337 | 0.025717 | 0.017106 | 0.01745 | −1.47762 | −1.96963 |
150 | 0.038006 | 0.038575 | 0.021497 | 0.021934 | −1.47634 | −1.99416 |
200 | 0.050674 | 0.051435 | 0.024836 | 0.025375 | −1.47954 | −2.12571 |
250 | 0.063343 | 0.064294 | 0.027727 | 0.028195 | −1.47992 | −1.66093 |
F (m) | EFG Linear Solution (w/m) | ANSYS Linear Solution (w/m) | EFG Nonlinear Solution (w/m) | ANSYS Nonlinear Solution (w/m) | Relative Error of Linear Solution (%) | Relative Error of Nonlinear Solution (%) |
---|---|---|---|---|---|---|
0.004 | 0.026359 | 0.026887 | 0.017539 | 0.01835 | −1.96526 | −4.41962 |
0.006 | 0.025337 | 0.025785 | 0.017106 | 0.018208 | −1.73744 | −6.05064 |
0.008 | 0.024022 | 0.024384 | 0.016534 | 0.017819 | −1.48335 | −7.20916 |
0.010 | 0.02251 | 0.022787 | 0.015852 | 0.017378 | −1.21692 | −8.77892 |
0.015 | 0.018434 | 0.018528 | 0.013866 | 0.015538 | −0.50518 | −10.7607 |
0.020 | 0.014664 | 0.014625 | 0.011775 | 0.013224 | 0.263932 | −10.9566 |
0.025 | 0.011573 | 0.01145 | 0.009834 | 0.010869 | 1.075109 | −9.52544 |
0.030 | 0.009172 | 0.009001 | 0.008148 | 0.008795 | 1.899345 | −7.35873 |
0.035 | 0.007342 | 0.007149 | 0.006743 | 0.007074 | 2.69786 | −4.68476 |
0.040 | 0.005951 | 0.00575 | 0.005597 | 0.005725 | 3.490435 | −2.24192 |
0.045 | 0.004885 | 0.004688 | 0.004674 | 0.004682 | 4.211391 | −0.17514 |
0.050 | 0.004063 | 0.003874 | 0.003933 | 0.003874 | 4.87842 | 1.530718 |
P (Pa) | EFG Linear Solution (w/m) | ANSYS Linear Solution (w/m) | EFG Nonlinear Solution (w/m) | ANSYS Nonlinear Solution (w/m) | Relative Error of Linear Solution (%) | Relative Error of Nonlinear Solution (%) |
---|---|---|---|---|---|---|
25 | 0.021303 | 0.021565 | 0.014526 | 0.013974 | −1.21725 | 3.953056 |
50 | 0.042605 | 0.043131 | 0.021289 | 0.021346 | −1.21977 | −0.26937 |
75 | 0.063907 | 0.064696 | 0.025818 | 0.026334 | −1.21893 | −1.96134 |
100 | 0.08521 | 0.086261 | 0.029322 | 0.029484 | −1.21851 | −0.54979 |
125 | 0.106512 | 0.107827 | 0.032257 | 0.03342 | −1.21955 | −3.48025 |
P (Pa) | EFG Linear Solution (w/m) | ANSYS Linear Solution (w/m) | EFG Nonlinear Solution (w/m) | ANSYS Nonlinear Solution (w/m) | Relative Error of Linear Solution (%) | Relative Error of Nonlinear Solution (%) |
---|---|---|---|---|---|---|
25 | 0.021303 | 0.021352 | 0.014526 | 0.01461 | −0.23183 | −0.57221 |
50 | 0.042605 | 0.042705 | 0.021289 | 0.021411 | −0.2344 | −0.57214 |
75 | 0.063907 | 0.064058 | 0.025818 | 0.025963 | −0.2351 | −0.56041 |
100 | 0.08521 | 0.085411 | 0.029322 | 0.029484 | −0.23545 | −0.54979 |
125 | 0.106512 | 0.106765 | 0.032257 | 0.0324 | −0.23697 | −0.44167 |
W (m) | EFG Linear Solution (w/m) | ANSYS Linear Solution (w/m) | EFG Nonlinear Solution (w/m) | ANSYS Nonlinear Solution (w/m) | Relative Error of Linear Solution (%) | Relative Error of Nonlinear Solution (%) |
---|---|---|---|---|---|---|
1.5 | 0.027784 | 0.017167 | 0.027643 | 0.016175 | 0.50863 | 6.13230 |
1.8 | 0.042224 | 0.021207 | 0.042289 | 0.021398 | −0.15347 | −0.89307 |
2.1 | 0.056862 | 0.024546 | 0.056859 | 0.025291 | 0.00475 | −2.94453 |
2.4 | 0.070602 | 0.027482 | 0.070818 | 0.028572 | −0.30557 | −3.81457 |
2.7 | 0.082882 | 0.030141 | 0.083039 | 0.031475 | −0.18907 | −4.23987 |
3.0 | 0.093516 | 0.032616 | 0.093830 | 0.034148 | −0.33422 | −4.48665 |
3.3 | 0.102536 | 0.034984 | 0.102778 | 0.036661 | −0.23546 | −4.57352 |
3.6 | 0.110080 | 0.037418 | 0.110408 | 0.039058 | −0.29708 | −4.19863 |
3.9 | 0.116325 | 0.039686 | 0.116572 | 0.041393 | −0.21189 | −4.12437 |
4.2 | 0.121457 | 0.041876 | 0.121740 | 0.043642 | −0.23246 | −4.04633 |
4.5 | 0.125647 | 0.043999 | 0.125853 | 0.045842 | −0.16368 | −4.02011 |
4.8 | 0.129048 | 0.045940 | 0.129266 | 0.047966 | −0.16864 | −4.22403 |
5.1 | 0.131794 | 0.047955 | 0.131956 | 0.050033 | −0.12277 | −4.15426 |
5.4 | 0.133997 | 0.049912 | 0.134171 | 0.052029 | −0.12969 | −4.0685 |
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Peng, L.; Zhang, Z.; Wei, D.; Tang, P.; Mo, G. Nonlinear Analysis of Corrugated Core Sandwich Plates Using the Element-Free Galerkin Method. Buildings 2025, 15, 1235. https://doi.org/10.3390/buildings15081235
Peng L, Zhang Z, Wei D, Tang P, Mo G. Nonlinear Analysis of Corrugated Core Sandwich Plates Using the Element-Free Galerkin Method. Buildings. 2025; 15(8):1235. https://doi.org/10.3390/buildings15081235
Chicago/Turabian StylePeng, Linxin, Zhaoyang Zhang, Dongyan Wei, Peng Tang, and Guikai Mo. 2025. "Nonlinear Analysis of Corrugated Core Sandwich Plates Using the Element-Free Galerkin Method" Buildings 15, no. 8: 1235. https://doi.org/10.3390/buildings15081235
APA StylePeng, L., Zhang, Z., Wei, D., Tang, P., & Mo, G. (2025). Nonlinear Analysis of Corrugated Core Sandwich Plates Using the Element-Free Galerkin Method. Buildings, 15(8), 1235. https://doi.org/10.3390/buildings15081235