Dynamic stability analysis of porous functionally graded beams under hygro-thermal loading using nonlocal strain gradient integral model

doi:10.1007/s10483-023-3059-9

Applied Mathematics and Mechanics (English Edition) ›› 2023, Vol. 44 ›› Issue (12): 2071-2092.doi: https://doi.org/10.1007/s10483-023-3059-9

Dynamic stability analysis of porous functionally graded beams under hygro-thermal loading using nonlocal strain gradient integral model

Pei ZHANG¹, P. SCHIAVONE², Hai QING³

1. School of Science, Xi'an University of Architecture and Technology, Xi'an 710055, China;
2. Department of Mechanical Engineering, University of Alberta, Edmonton T6G 1H9, Alberta, Canada;
3. State Key Laboratory of Mechanics and Control for Aerospace Structures, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China

收稿日期:2023-07-04 修回日期:2023-10-08 发布日期:2023-11-27
通讯作者: Hai QING, E-mail: qinghai@nuaa.edu.cn
基金资助:
the National Natural Science Foundation of China (No. 12172169) and the Natural Sciences and Engineering Research Council of Canada (No. NSERC RGPIN-2023-03227)

Dynamic stability analysis of porous functionally graded beams under hygro-thermal loading using nonlocal strain gradient integral model

Pei ZHANG¹, P. SCHIAVONE², Hai QING³

1. School of Science, Xi'an University of Architecture and Technology, Xi'an 710055, China;
2. Department of Mechanical Engineering, University of Alberta, Edmonton T6G 1H9, Alberta, Canada;
3. State Key Laboratory of Mechanics and Control for Aerospace Structures, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China

Received:2023-07-04 Revised:2023-10-08 Published:2023-11-27
Contact: Hai QING, E-mail: qinghai@nuaa.edu.cn
Supported by:
the National Natural Science Foundation of China (No. 12172169) and the Natural Sciences and Engineering Research Council of Canada (No. NSERC RGPIN-2023-03227)

摘要/Abstract

摘要： We present a study on the dynamic stability of porous functionally graded (PFG) beams under hygro-thermal loading. The variations of the properties of the beams across the beam thicknesses are described by the power-law model. Unlike most studies on this topic, we consider both the bending deformation of the beams and the hygro-thermal load as size-dependent, simultaneously, by adopting the equivalent differential forms of the well-posed nonlocal strain gradient integral theory (NSGIT) which are strictly equipped with a set of constitutive boundary conditions (CBCs), and through which both the stiffness-hardening and stiffness-softening effects of the structures can be observed with the length-scale parameters changed. All the variables presented in the differential problem formulation are discretized. The numerical solution of the dynamic instability region (DIR) of various bounded beams is then developed via the generalized differential quadrature method (GDQM). After verifying the present formulation and results, we examine the effects of different parameters such as the nonlocal/gradient length-scale parameters, the static force factor, the functionally graded (FG) parameter, and the porosity parameter on the DIR. Furthermore, the influence of considering the size-dependent hygro-thermal load is also presented.

关键词: nonlocal strain gradient integral model, dynamic stability, porous functionally graded (PFG) shear deformation beam, size-dependent hygro-thermal load, generalized differential quadrature method (GDQM)

Abstract: We present a study on the dynamic stability of porous functionally graded (PFG) beams under hygro-thermal loading. The variations of the properties of the beams across the beam thicknesses are described by the power-law model. Unlike most studies on this topic, we consider both the bending deformation of the beams and the hygro-thermal load as size-dependent, simultaneously, by adopting the equivalent differential forms of the well-posed nonlocal strain gradient integral theory (NSGIT) which are strictly equipped with a set of constitutive boundary conditions (CBCs), and through which both the stiffness-hardening and stiffness-softening effects of the structures can be observed with the length-scale parameters changed. All the variables presented in the differential problem formulation are discretized. The numerical solution of the dynamic instability region (DIR) of various bounded beams is then developed via the generalized differential quadrature method (GDQM). After verifying the present formulation and results, we examine the effects of different parameters such as the nonlocal/gradient length-scale parameters, the static force factor, the functionally graded (FG) parameter, and the porosity parameter on the DIR. Furthermore, the influence of considering the size-dependent hygro-thermal load is also presented.

Key words: nonlocal strain gradient integral model, dynamic stability, porous functionally graded (PFG) shear deformation beam, size-dependent hygro-thermal load, generalized differential quadrature method (GDQM)

中图分类号:

74K10

Pei ZHANG, P. SCHIAVONE, Hai QING. Dynamic stability analysis of porous functionally graded beams under hygro-thermal loading using nonlocal strain gradient integral model[J]. Applied Mathematics and Mechanics (English Edition), 2023, 44(12): 2071-2092.

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Dynamic stability analysis of porous functionally graded beams under hygro-thermal loading using nonlocal strain gradient integral model

Dynamic stability analysis of porous functionally graded beams under hygro-thermal loading using nonlocal strain gradient integral model

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