A Superconvergent Isogeometric Method with Refined Quadrature for Buckling Analysis of Thin Beams and Plates

2021 ◽  
pp. 2150153
Author(s):  
Xiaolan Xu ◽  
Dongdong Wang ◽  
Xiwei Li ◽  
Songyang Hou ◽  
Jianguo Zhang
Keyword(s):  
Thin Plate ◽  
Stiffness Matrix ◽  
Quadrature Rule ◽  
Buckling Analysis ◽  
Buckling Load ◽  
Buckling Loads ◽  
Buckling Modes ◽  
Geometric Stiffness ◽  
Material Stiffness ◽  
Thin Beams

A superconvergent isogeometric method is developed for the buckling analysis of thin beams and plates, in which the quadratic basis functions are particularly considered. This method is formulated through refining the quadrature rules used for the numerical integration of geometric and material stiffness matrices. The criterion for the quadrature refinement is the optimization of the buckling load accuracy under the assumption of harmonic buckling modes for thin beams and plates. The method development starts with the thin beam buckling analysis, where the material stiffness matrix with quadratic basis functions does not involve numerical integration and thus the refined quadrature rule for geometric stiffness matrix can be obtained in a relatively easy way. Subsequently, this refined quadrature rule for thin beam geometric stiffness matrix is conveniently generalized to the thin plate geometric stiffness matrix via the tensor product operation. Meanwhile, the refined quadrature rule for the thin plate material stiffness matrix is derived by minimizing the buckling load error. It turns out that the refined quadrature rule for the thin plate material stiffness matrix generally depends on the wave numbers of buckling modes. A theoretical error analysis for the buckling loads evinces that the isogeometric method with refined quadrature rules offers a fourth-order accurate superconvergent algorithm for buckling load computation, which is two orders higher than the standard isogeometric analysis approach. Numerical results well demonstrate the superconvergence of the proposed method for the buckling loads corresponding to harmonic buckling modes, and for those related with non-harmonic modes, the buckling loads given by the proposed method are also much more accurate than their counterparts produced by the conventional isogeometric analysis.

Buckling Analysis of Symmetric Cross-Ply Laminated Annular Plates with Carbon Nanotubes

2014 ◽  
Vol 592-594 ◽  
pp. 901-905
Author(s):  
Pankaj Kumar ◽  
Pandey Ramesh
Keyword(s):  
Carbon Nanotubes ◽  
Boundary Condition ◽  
Carbon Nanotube ◽  
Aspect Ratio ◽  
Energy Method ◽  
Buckling Analysis ◽  
Buckling Load ◽  
Buckling Loads ◽  
Annular Plates ◽  
Buckling Behavior

The Paper presents the buckling response of composite annular plates with under uniform internal and external radial edge loads using energy method. For the equation of stability Trefftez rule is used. The paper consists of buckling behavior of laminate (90/0) s, influence of some parameters such as thickness, boundary condition, aspect ratio on buckling loads and modes are investigated. Present results are compared with other papers. In this paper the effect of % weight of carbon nanotube (MWCNT) on the buckling load is also investigated.

BUCKLING OF COLUMNS WITH INTERNAL SLIDE RELEASE

2002 ◽  
Vol 02 (04) ◽  
pp. 593-598 ◽  
Author(s):  
M. EISENBERGER ◽  
H. AMBARSUMIAN
Keyword(s):  
Stiffness Matrix ◽  
Buckling Load ◽  
Buckling Loads ◽  
Simply Supported ◽  
Axial Forces ◽  
Exact Stiffness Matrix

The exact buckling loads of columns with internal slide release are found using the exact stiffness matrix of the column including the effect of the axial forces. Two types of columns are considered: clamped–clamped and clamped-simply supported with internal slide release at variable locations along the member. It is found that for both the clamped–clamped and the clamped-simply supported columns the buckling load is constant and does not depend on the location of the slide discontinuity.

Effects of the prestress levels on the stiffness of prismatic and star-shaped tensegrity structures

2016 ◽  
Vol 22 (9) ◽  
pp. 1866-1875 ◽  
Author(s):  
Jianguo Cai ◽  
Yuhang Zhou ◽  
Jian Feng ◽  
Xiaowei Deng ◽  
Yongming Tu
Keyword(s):  
Stiffness Matrix ◽  
Eigenvalue Analysis ◽  
Numerical Examples ◽  
Tensegrity Structures ◽  
Tensegrity Structure ◽  
Geometric Stiffness ◽  
Analytical Results ◽  
Material Stiffness

On the basis of the introduction of the stiffness matrix of tensegrity structures, the eigenvalue analysis is carried out to study the influence of the prestress level on the stiffness of tensegrity structures. The triangular prismatic tensegrity structure, the star-shaped tensegrity structure and the star-shaped tensegrity structure with a central strut are selected as the numerical examples. The analytical results show that some eigenvalues increase linearly with the prestress level, whereas other eigenvalues firstly increase and then decrease or firstly decrease and then increase with the increase of the prestress level. This is because the stiffness matrix of the tensegrity structures is mainly composed of the material stiffness matrix and geometric stiffness matrix. As the contribution of these two parts of stiffness to eigenvalue models is different, the trends of eigenvalue variations are different with the increase of the prestressed level.

scholarly journals Experimental and Numerical Studies on the Shear Stability of Ship’s Thin Plates

2021 ◽  
Vol 28 (4) ◽  
pp. 133-141
Author(s):  
Xiaowen Li ◽  
Zhaoiy Zhu ◽  
Qinglin Chen ◽  
Yingqiang Cai ◽  
Miaojiao Peng
Keyword(s):  
Numerical Simulation ◽  
Thin Plate ◽  
Buckling Analysis ◽  
Buckling Load ◽  
Thin Plates ◽  
Displacement Curve ◽  
Plane Shear ◽  
Critical Buckling Load ◽  
Full Field ◽  
Shear Stability

Abstract The stability of thin plate plays an important role in the design and strength check of ship structure. In order to study the shear stability of ship’s thin plates, in-plane shear buckling tests were carried out using a picture frame fixture and a 3D full-field strain measurement system. The critical buckling load, full-field displacement/strain information, and load-displacement curve were obtained. The finite element model with the frame fixture was established based on ABAQUS, with the eigenvalue buckling analysis and nonlinear buckling analysis being carried out to obtain the mechanical response information of the buckling and post-buckling of the ship’s thin plate. The effectiveness and accuracy of the numerical simulation method are verified by comparing the numerical simulation with the experimental results. On this basis, the critical buckling load obtained by shear test, numerical simulation, and theoretical calculation is analyzed, and the function of the frame shear fixture and its influence on the critical buckling load are defined. The research in this paper provides a useful reference for the testing and simulation of in-plane shear stability of ship’s thin plates.

A Method for System Buckling Analysis of Plane Sway Frame

2015 ◽  
Vol 21 ◽  
pp. 1-18
Author(s):  
Kui Nian Li
Keyword(s):  
Stiffness Matrix ◽  
Practical Method ◽  
Buckling Analysis ◽  
Buckling Load ◽  
Negative Stiffness ◽  
Simple Method ◽  
Order Analysis ◽  
First Order ◽  
Modification Factor ◽  
Analysis Application

Presented in this paper is a simple and practical method for buckling analysis of the overall structural system. The method is developed from the idea that the stiffness (for a SDOF system) or determinant of stiffness matrix (for a MDOF system) is getting to zero as the system is loaded to bucking mode, or the loads reaches the buckling load of the system. A negative stiffness (matrix) is introduced to take the effect of axial loads on the stiffness (matrix) of the system into account and the stiffness (matrix) is modified by this negative stiffness (matrix). To get the buckling load of the overall system, first order analysis (P-Δeffect) is performed with a simple method suggested. The second order analysis (P-δ) is performed by the introducing of a force modification factor to modify the buckling load from first order analysis. Application examples are presented and the results are compared with result obtained from system buckling analysis with FEA. The simplicity, effectiveness and the accuracy of the suggested method is demonstrated.

Flexural-Torsional Buckling of Pultruded Fiber-Reinforced Polymer Angle Beams under Eccentric Loading

2020 ◽  
Vol 982 ◽  
pp. 201-206
Author(s):  
Jaksada Thumrongvut ◽  
Natthawat Pakwan ◽  
Samaporn Krathumklang
Keyword(s):  
Buckling Load ◽  
Fiber Reinforced Polymer ◽  
Width Ratio ◽  
Fiber Reinforced ◽  
Torsional Buckling ◽  
Eccentric Load ◽  
Buckling Loads ◽  
Reinforced Polymer ◽  
Cross Sectional Dimension ◽  
Flexural Torsional Buckling

In this paper, the experimental study on the pultruded fiber-reinforced polymer (pultruded FRP) angle beams subjected to transversely eccentric load are presented. A summary of critical buckling load and buckling behavior for full-scale flexure tests with various span-to-width ratios (L/b) and eccentricities are investigated, and typical failure mode are identified. Three-point flexure tests of 50 pultruded FRP angle beams are performed. The E-glass fibre/polyester resin angle specimens are tested to examine the effect of span-to-width ratio of the beams on the buckling responses and critical buckling loads. The angle specimens have the cross-sectional dimension of 76x6.4 mm with span-to-width ratios, ranging from 20 to 40. Also, four different eccentricities are investigated, ranging from 0 to ±2e. Eccentric loads are applied below the horizontal flange in increments until beam buckling occurred. Based upon the results of this study, it is found that the load and mid-span vertical deflection relationships of the angle beams are linear up to the failure. In contrast, the load and mid-span lateral deflection relationships are geometrically nonlinear. The general mode of failure is the flexural-torsional buckling. The eccentrically loaded specimens are failed at critical buckling loads lower than their concentric counterparts. Also, the quantity of eccentricity increases as buckling load decreases. In addition, it is noticed that span-to-width ratio increases, the buckling load is decreased. The eccentric location proved to have considerable influence over the buckling load of the pultruded FRP angle beams.

Consistent co-rotational framework for Euler-Bernoulli and Timoshenko beam-column elements under distributed member loads

2021 ◽  
pp. 136943322098663
Author(s):  
Yi-Qun Tang ◽  
Wen-Feng Chen ◽  
Yao-Peng Liu ◽  
Siu-Lai Chan
Keyword(s):  
Coordinate System ◽  
Stiffness Matrix ◽  
Traditional Method ◽  
Local Coordinate System ◽  
Frame Structures ◽  
Global Coordinate System ◽  
Single Element ◽  
Geometrically Nonlinear ◽  
Geometrically Nonlinear Analysis ◽  
Geometric Stiffness

Conventional co-rotational formulations for geometrically nonlinear analysis are based on the assumption that the finite element is only subjected to nodal loads and as a result, they are not accurate for the elements under distributed member loads. The magnitude and direction of member loads are treated as constant in the global coordinate system, but they are essentially varying in the local coordinate system for the element undergoing a large rigid body rotation, leading to the change of nodal moments at element ends. Thus, there is a need to improve the co-rotational formulations to allow for the effect. This paper proposes a new consistent co-rotational formulation for both Euler-Bernoulli and Timoshenko two-dimensional beam-column elements subjected to distributed member loads. It is found that the equivalent nodal moments are affected by the element geometric change and consequently contribute to a part of geometric stiffness matrix. From this study, the results of both eigenvalue buckling and second-order direct analyses will be significantly improved. Several examples are used to verify the proposed formulation with comparison of the traditional method, which demonstrate the accuracy and reliability of the proposed method in buckling analysis of frame structures under distributed member loads using a single element per member.

scholarly journals CFRP Origami Metamaterial with Tunable Buckling Loads: A Numerical Study

Materials ◽  
2021 ◽  
Vol 14 (4) ◽  
pp. 917
Author(s):  
Houyao Zhu ◽  
Shouyan Chen ◽  
Teng Shen ◽  
Ruikun Wang ◽  
Jie Liu
Keyword(s):  
Numerical Study ◽  
Buckling Load ◽  
Fe Modelling ◽  
Buckling Loads ◽  
Folding Angle ◽  
Mechanical Responses ◽  
Reinforced Plastic ◽  
Rate Of Increase ◽  
Practical Engineering ◽  
Identical Rate

Origami has played an increasingly central role in designing a broad range of novel structures due to its simple concept and its lightweight and extraordinary mechanical properties. Nonetheless, most of the research focuses on mechanical responses by using homogeneous materials and limited studies involving buckling loads. In this study, we have designed a carbon fiber reinforced plastic (CFRP) origami metamaterial based on the classical Miura sheet and composite material. The finite element (FE) modelling process’s accuracy is first proved by utilizing a CFRP plate that has an analytical solution of the buckling load. Based on the validated FE modelling process, we then thoroughly study the buckling resistance ability of the proposed CFRP origami metamaterial numerically by varying the folding angle, layer order, and material properties, finding that the buckling loads can be tuned to as large as approximately 2.5 times for mode 5 by altering the folding angle from 10° to 130°. With the identical rate of increase, the shear modulus has a more significant influence on the buckling load than Young’s modulus. Outcomes reported reveal that tunable buckling loads can be achieved in two ways, i.e., origami technique and the CFRP material with fruitful design freedoms. This study provides an easy way of merely adjusting and controlling the buckling load of lightweight structures for practical engineering.

RELIABILITY ASSESSMENT OF AXIALLY COMPRESSED COMPOSITE CYLINDRICAL SHELLS WITH RANDOM IMPERFECTIONS

2011 ◽  
Vol 11 (02) ◽  
pp. 215-236 ◽  
Author(s):  
MATTEO BROGGI ◽  
ADRIANO CALVI ◽  
GERHART I. SCHUËLLER
Keyword(s):  
Mathematical Models ◽  
Axial Compression ◽  
Cylindrical Shells ◽  
Reliability Assessment ◽  
Buckling Analysis ◽  
Buckling Load ◽  
Experimental Results ◽  
Drastic Decrease ◽  
Different Types ◽  
Probability And Statistics

Cylindrical shells under axial compression are susceptible to buckling and hence require the development of enhanced underlying mathematical models in order to accurately predict the buckling load. Imperfections of the geometry of the cylinders may cause a drastic decrease of the buckling load and give rise to the need of advanced techniques in order to consider these imperfections in a buckling analysis. A deterministic buckling analysis is based on the use of the so-called knockdown factors, which specifies the reduction of the buckling load of the perfect shell in order to account for the inherent uncertainties in the geometry. In this paper, it is shown that these knockdown factors are overly conservative and that the fields of probability and statistics provide a mathematical vehicle for realistically modeling the imperfections. Furthermore, the influence of different types of imperfection on the buckling load are examined and validated with experimental results.

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