应用数学和力学

2024 Vol. 45, No. 4

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Solid Mechanics
Interdisciplinary Mechanics
Applied Mathematics

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2024, 45(4)

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Solid Mechanics

Software Development for Stand Seam Roof Systems Based on the LiToSim Platform

LIU Min, LIU Xiang, FENG Zhiqiang, GU Shuitao

2024, 45(4): 379-390. doi: 10.21656/1000-0887.440150

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Abstract:
The stand seam roof is prone to failure under wind pressure. There is a lack of mechanical models and finite element analysis software that can numerically simulate the wind-induced response of stand seam roof systems. Firstly, the elastoplastic equivalent spring model for the stand seam roof was proposed according to the nonlinear wind-induced response of the structure, and the finite element algorithm for the elastoplastic equivalent spring element was derived, then the algorithm was embedded in the LiToSim platform to develop customized software LiToSpr for the stand seam roof. Finally, the structural responses were modeled, analyzed and compared with the anti-wind unmasking experiment results, to verify the applicability of customized software LiToSpr. The research indicates that, software LiToSpr can well simulate the wind-induced responses of the stand seam roof, and provides a reference for engineering design.

A Three-Dimensional Adaptive Finite Element Method for Phase-Field Models of Fracture

QIU Shasha, LIU Xingze, NING Wenjie, YAO Weian, DUAN Qinglin

2024, 45(4): 391-399. doi: 10.21656/1000-0887.440299

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Abstract:
A robust predictor-corrector algorithm was developed and a 3D adaptive finite element analysis for the fracture phase-field model was established. This model can deal with complex fracture problems conveniently, avoiding extra tracking of crack paths and without mesh-dependency. However, the 3D phase-field modeling usually requires extremely fine meshes, which brings reduction of the solving efficiency. Aimed at this problem, the predictor-corrector adaptive mesh refinement algorithm was developed based on a staggered solution scheme, to achieve high-precision analysis of crack propagation in 3D structures. Numerical examples show that, the developed method can accurately and reasonably describe crack propagation in structures, and the meshes can be adaptively refined along the crack propagation paths.

Boundary Element Analysis for the Plane Elasticity Problems of Finite Icosahedral Quasicrystal Plates Containing Elliptical Holes

WANG Huiping, WANG Guixia, CHEN Decai

2024, 45(4): 400-415. doi: 10.21656/1000-0887.440241

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Abstract:
Based on the extended Stroh method, a boundary element analysis was conducted for the plane elasticity problem of finite-sized icosahedral quasicrystal plates with elliptical holes. Firstly, the extended Stroh method was used to study Green's function for the icosahedral quasicrystal, to obtain the fundamental solutions of displacements and stresses of the plane elasticity problem about infinite-sized icosahedral quasicrystal plates with elliptical holes. With these fundamental solutions, the weighted residual method was employed to establish the integral equations within the domain and on the boundary, and the linear interpolation functions and the Gaussian integration were used to discretize the boundary integral equations and the domain integral equations with unknown variables, respectively. Furthermore, the stress at the hole boundary was numerically solved, and the numerical results of the finite-sized plate were compared with the analytical solution of the infinite-sized plate to demonstrate that, the analytical solution of the infinite-sized plate cannot be used for the analysis of the finite-sized plate with the ratio of the plate size to the hole size below a certain threshold. Finally, the effects of the plate size, the hole size, and the inclination angle on the stress at the hole boundary were analyzed under tensile loading in the vertical direction. The results show that, the variation of the plate size along the vertical tensile direction has a more significant effect on the stress at the hole boundary. As the elliptical hole size increases, the stress concentration phenomenon becomes more pronounced. If the major axis is perpendicular to the vertical tensile direction, the inclination of the elliptical hole will mitigate the degree of stress concentration at the hole boundary.

Interdisciplinary Mechanics

Research on Bridge Performance Degradation Prediction Based on Combination of the D-S Theory and the Markov Chain

YANG Guojun, TIAN Li, TANG Guangwu, MAO Jianbo, DU Yongfeng

2024, 45(4): 416-428. doi: 10.21656/1000-0887.440343

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Abstract:
To accurately predict bridge performance degradation, the inherent data randomness and the subtle perturbations leading to state transitions were considered. A combined prediction method for the bridge performance degradation based on the D-S theory and the Markov chain, and the performance degradation rate concept, were proposed. In this model, the exponential smoothing (ES) methodology was employed as the basis for generating new sequences of predictive data. It was continuously optimized through the utilization of the Markov chains and the Dempster-Shafer (D-S) evidence theory. The combined prediction of bridge performance degradation was achieved. The application results from practical engineering show that, the performance degradation rate serves as an intuitive indicator of the speed at which the bridge performance degrades. Subsequently, the combined model demonstrates an average relative error of 1.54%, improves by 1.11%, 0.88%, and 2.8% in accuracy, respectively in comparison with other models of the regression, the grey system, and the fuzzy weighted Markov chain. Additionally, the calculated posterior difference ratio is 0.242, well below the established threshold of 0.35. In terms of stability, the standard deviation of the model is 9.021, reduces by 3.978, 3.405 and 7.500, respectively compared with those of the other 3 models. The coefficient of variation is 0.109, indicating a significant reduction in comparison to those of the other models. The combined prediction model, with verified accuracy and stability, establishes a theoretical foundation for prediction and maintenance of in-service bridges' structural performance degradation.

A Defect Identification Method for Bonding Layers of Adhesive Steel Members Based on Machine Learning

YAO Hao, XIA Guiran, LIU Zejia, ZHOU Licheng

2024, 45(4): 429-442. doi: 10.21656/1000-0887.440365

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Abstract:
The effects of bonding layer defects on ultrasonic detection signals of bonded steel reinforced structures were deeply studied and a new method for the bonding layer defect identification based on machine learning was proposed. Firstly, based on the direct contact pulse-echo reflection method, the finite element simulation of the viscous steel member was carried out, and the propagation law of ultrasonic waves in the viscous steel member was expounded. Secondly, the characteristics of local ultrasonic echo signals and related signals were analyzed, and the effects of different defect variables on ultrasonic echo signals were discussed. Finally, the ultrasonic time-history response data set of the adhesive steel member was established, and the classification and recognition performances of different machine learning models for the size and location of defects were compared, and the defect identification method for the adhesive layer of the bonded steel member was built. The results show that, the local ultrasonic echo signal and its characteristics change regularly with the defect size and location, which can help preliminarily distinguish the defect information. Meanwhile, the proposed RF model-based defect identification method can effectively identify the defects of the adhesive layer in the bonded steel member, and has a broad engineering application prospect.

A Random Forest Evaluation Model for Pavement Skid Resistance Based on Comprehensive Fractal

PENG Yi, ZHANG Zhengqi, LI Qiang, YANG Guangwei

2024, 45(4): 443-457. doi: 10.21656/1000-0887.440244

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Abstract:
The pavement anti-skid performance directly affects road traffic safety, and the evaluation methods based on pavement texture features currently have problems of poor interpretability and low accuracy. Herein, 185 sets of pavement texture data were collected by the portable 3D laser surface analyzer with an accuracy of 0.05 mm. The pavement friction data in the speed range of 0~80 km/h of the corresponding road section were obtained with the dynamic friction coefficient tester. The comprehensive fractal dimension index representing the complexity of the pavement texture space, the cross section, and the depth direction was constructed, and the random forest evaluation model for pavement skid resistance performances at speeds of 10 km/h and 70 km/h. The results show that, the comprehensive fractal dimension has the ability to describe the complexity of texture independently, but there is no linear relationship between it and the pavement dynamic friction coefficient; the prediction accuracy of comprehensive fractal dimensions for dynamic friction coefficients at the 70 km/h speed is 0.78, which can be used to evaluate the skid resistance of pavement under the condition of rapid sliding of tire rubber; the spatial, cross-sectional, surface, shallow, and deep profile fractal features in comprehensive fractal indicators jointly affect the pavement anti-skid performances. In the evaluation of pavement texture morphology, comprehensive analysis of texture features should be conducted from multiple spatial perspectives.

Non-Probabilistic Reliability Indexes Based on the Generalized Super Ellipsoid Model

QIAO Xinzhou, ZHAO Yuetong, FANG Xiurong, LIU Peng

2024, 45(4): 458-469. doi: 10.21656/1000-0887.440061

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Abstract:
The non-probabilistic convex model only requires the bounds or domains of structural uncertain parameters to measure structural reliability, and therefore is more appropriate for engineering structures with limited experimental data. The problem of non-probabilistic reliability measurement of the generalized super ellipsoid model was studied. A simple non-probabilistic reliability index was first proposed to evaluate the safety degree of a structure, which was defined as the ratio of the mean value of the performance function to its deviation. The inconsistency problem in the simple non-probabilistic reliability index was further discussed. To overcome the above inconsistency problem, a ratio factor reliability index was then presented, which was defined as the minimum ratio factor at which the failure surface is in contact with the uncertainty domain contracting inward or expanding outward. Three numerical examples demonstrate the validity and feasibility of the proposed non-probabilistic reliability indexes.

Applied Mathematics

A Class of Right-Hand Discontinuous Singularly Perturbed Boundary Value Problems With Turning Points

SHUAI Xin, NI Mingkang

2024, 45(4): 470-489. doi: 10.21656/1000-0887.440353

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Abstract:
The asymptotic behavior of solutions to a class of right-hand discontinuous 2nd-order semilinear singularly perturbed boundary value problems with turning points was studied. Firstly, the original problem was divided into left and right problems at the discontinuity, the accuracy of the asymptotic solution to the left problem was improved through modification of the regularization equation for the left problem degradation problem, and the existence of the smooth solution to the left problem was proved by means of the Nagumo theorem. Secondly, the solution to the right problem was proved to have a spatial contrast structure, and the asymptotic solution to the original problem was obtained through smooth joints at the discontinuity points. Finally, the correctness of the results was verified by an example.

A Continuous Space-Time Mixed Finite Element Method for Sine-Gordon Equations

WANG Chunyuan, LI Hong, HE Siriguleng

2024, 45(4): 490-501. doi: 10.21656/1000-0887.440293

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Abstract:
The mixed finite element method was combined with the continuous space-time finite element method to construct a continuous space-time mixed finite element scheme for sine-Gordon equations, through the introduction of independent variable p=u_t to solve the equations. This scheme uses the finite element method to treat both time and space variables. The space-time mixed finite element scheme can reduce the order of the equation and lower the smoothness requirements on the finite element space. The advantages of the finite element method was utilized in both the time and the space directions, thereby to obtain high-precision space-time numerical solutions. The stability of numerical solutions was strictly proven in the theoretical analysis, and error estimates for u and p were provided. Finally, the effectiveness and feasibility of the proposed method were demonstrated through numerical examples.

Higher-Order KKT Sufficient Optimality Conditions for Nonsmooth Semi-Infinite Multiobjective Optimization

CAO Qi, FENG Min

2024, 45(4): 502-508. doi: 10.21656/1000-0887.440245

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Abstract:
The nonsmooth semi-infinite multiobjective optimization problems were investigated. The higher-order weak KKT sufficient optimality conditions for strictly local efficient solutions were established in terms of higher-order lower Studniarski derivatives. Furthermore, under the assumption that all multipliers associated with objective functions are positive in optimality conditions, the higher-order strong KKT sufficient optimality conditions for strictly local Borwein-properly efficient solutions would be achieved. These sufficient optimality conditions were established without any convexity assumptions.