New Ritz-solution shape functions for analysis of thermo-mechanical buckling and vibration of laminated composite beams

Nguyen, Ngoc-Duong; Nguyen, Thanh Thuy; Nguyen, Thien-Nhan; Thai, Huu‐Tai

doi:10.1016/j.compstruct.2017.10.003

Cited by 40 publications

(15 citation statements)

References 31 publications

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“…Among different numerical approaches, in the present work we apply a Ritz-type solution with harmonic trial functions to solve the problem, whose stability and accuracy is verified through a systematic investigation. In line with predictions from the literature [65][66][67][68][69][70][71][72][73], the Rayleigh-Ritz method, represents an efficient tool for the analysis of the structural behavior of beams, whose accuracy and stability are well known to be related to the selected trial functions. The trial functions must satisfy the enforced boundary conditions.…”

Section: Introductionmentioning

confidence: 79%

A Modified Couple Stress Elasticity for Non-Uniform Composite Laminated Beams Based on the Ritz Formulation

et al. 2020

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Due to the large application of tapered beams in smart devices, such as scanning tunneling microscopes (STM), nano/micro electromechanical systems (NEMS/MEMS), atomic force microscopes (AFM), as well as in military aircraft applications, this study deals with the vibration behavior of laminated composite non-uniform nanobeams subjected to different boundary conditions. The micro-structural size-dependent free vibration response of composite laminated Euler–Bernoulli beams is here analyzed based on a modified couple stress elasticity, which accounts for the presence of a length scale parameter. The governing equations and boundary conditions of the problem are developed using the Hamilton’s principle, and solved by means of the Rayleigh–Ritz method. The accuracy and stability of the proposed formulation is checked through a convergence and comparative study with respect to the available literature. A large parametric study is conducted to investigate the effect of the length-scale parameter, non-uniformity parameter, size dimension and boundary conditions on the natural frequencies of laminated composite tapered beams, as useful for design and optimization purposes of small-scale devices, due to their structural tailoring capabilities, damage tolerance, and their potential for creating reduction in weight.

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Section: Introductionmentioning

confidence: 79%

A Modified Couple Stress Elasticity for Non-Uniform Composite Laminated Beams Based on the Ritz Formulation

et al. 2020

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“…Ngoài ra, Nguyễn, và cs. [22] đề xuất các hàm "Hybrid" dạng mũ và đa thức để phân tích dao động và ổn định của dầm composite chịu tải trọng cơ nhiệt. Có thể thấy rằng, sự hiệu quả của lời giải Ritz phụ thuộc vào đặc điểm của hàm dạng và lời giải này ít được sử dụng khi phân tích tĩnh dầm composite.…”

Section: Giới Thiệuunclassified

Phân tích tĩnh dầm composite sử dụng lý thuyết biến dạng cắt bậc cao hai biến

Nhân¹,

Dương²,

Kiên³

2020

TCKHCNXD

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Bài báo này đề xuất một lý thuyết biến dạng cắt bậc cao hai biến để phân tích ứng xử tĩnh của dầm composite. Trường chuyển vị của bài toán được rút gọn từ lý thuyết biến dạng cắt bậc cao ba biến bằng cách sử dụng phương trình cân bằng tĩnh học. Phương trình chủ đạo được thành lập từ phương trình Lagrange. Lời giải Ritz, với hàm xấp xỉ là hàm số mũ cơ số Napier, phù hợp với các điều kiện biên khác nhau được đề xuất để giải bài toán. Sự hiệu quả của trường chuyển vị đề xuất và hàm xấp xỉ Ritz mới được phân tích, đánh giá. Các ví dụ số được thực hiện để khảo sát độ hội tụ của lời giải và so sánh với các nghiên cứu trước. Ảnh hưởng của điều kiện biên, hướng sợi, tỷ số chiều dài/chiều cao dầm, đặc biệt là biến dạng cắt đến chuyển vị và ứng suất của dầm composite lớp được khảo sát và bình luận chi tiết. Từ khóa: dầm composite; lý thuyết biến dạng cắt bậc cao; phương pháp Ritz; phân tích tĩnh; rút gọn trường chuyển vị.

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“…Modifying the previous models with consideration of shearing, Eltaher et al [15,16] presented bending, vibration and buckling behavior of thick nanobeams under the mechanical loading. Nguyen et al [17] analyzed the thermo-mechanical vibrational and buckling behavior of LCB through novel shape function based on Ritz method. It must be noticed that, buckling can even appear in the ambience of non-uniform variable in plane loading conditions.…”

Section: Introductionmentioning

confidence: 99%

Buckling and vibration analysis of shape memory laminated composite beams under axially heterogeneous in-plane loads in the glass transition temperature region

Tiwari

Shaikh

2021

SN Appl. Sci.

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Buckling and vibration study of the shape memory polymer composites (SMPC) across the glass transition temperature under heterogeneous loading conditions are presented. Finite element analysis based on C° continuity equation through the higher order shear deformation theory (HSDT) is employed considering non linear Von Karman approach to estimate critical buckling and vibration for the temperature span from 273 to 373 K. Extensive numerical investigations are presented to understand the effect of temperature, boundary conditions, aspect ratio, fiber orientations, laminate stacking and modes of phenomenon on the buckling and vibration behavior of SMPC beam along with the validation and convergence study. Effect of thermal conditions, particularly in the glass transition region of the shape memory polymer, is considerable and presents cohesive relation between dynamic modulus properties with magnitude of critical buckling and vibration. Moreover, it has also been inferred that type of axial loading condition along with the corresponding boundary conditions significantly affect the buckling and vibration load across the glass transition region.

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New Ritz-solution shape functions for analysis of thermo-mechanical buckling and vibration of laminated composite beams

Cited by 40 publications

References 31 publications

A Modified Couple Stress Elasticity for Non-Uniform Composite Laminated Beams Based on the Ritz Formulation

A Modified Couple Stress Elasticity for Non-Uniform Composite Laminated Beams Based on the Ritz Formulation

Phân tích tĩnh dầm composite sử dụng lý thuyết biến dạng cắt bậc cao hai biến

Buckling and vibration analysis of shape memory laminated composite beams under axially heterogeneous in-plane loads in the glass transition temperature region

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