EXPLICIT LOCAL BUCKLING ANALYSIS OF ROTATIONALLY RESTRAINED COMPOSITE PLATES UNDER BIAXIAL LOADING

2007 ◽  
Vol 07 (03) ◽  
pp. 487-517 ◽  
Author(s):  
PIZHONG QIAO ◽  
LUYANG SHAN
Keyword(s):  
Composite Structures ◽  
Biaxial Loading ◽  
Ritz Method ◽  
Local Buckling ◽  
Composite Plates ◽  
Biaxial Compression ◽  
Thin Walled Structures ◽  
Special Cases ◽  
Rotational Restraint ◽  
Elastically Restrained

A variational formulation of the Ritz method is used to establish an eigenvalue problem for the local buckling behavior of composite plates elastically restrained (R) along their four edges (the RRRR plates) and subjected to biaxial compression, and the explicit solution in terms of the rotational restraint stiffness (k) is presented. Based on the different boundary and loading conditions, the explicit local buckling solution for the rotationally restrained plates is simplified to several special cases (e.g. the SSSS, SSCC, CCSS, CCCC, SSRR, RRSS, CCRR, and RRCC plates) under biaxial compression (and further reduced to uniaxial compression) with a combination of simply-supported (S), clamped (C), and/or restrained (R) edge conditions. The deformation shape function is presented by using the unique harmonic functions in both the axes to account for the effect of elastic rotational restraint stiffness (k) along the four edges of the orthotropic plate. A parametric study is conducted to evaluate the influences of the loading ratio (α), the rotational restraint stiffness (k), the aspect ratio (γ), and the flexural-orthotropy parameters (α OR and β OR ) on the local buckling stress resultants of various rotationally restrained plates, and design plots with respect to these parameters are provided. The present explicit local buckling solution of the elastically restrained composite plates and the associated design plots can be employed to facilitate design analysis of composite structures (e.g. stiffened panels, thin-walled structures, and honeycomb cores).

Maximizing the Fundamental Natural Frequency of Triangular Composite Plates

1996 ◽  
Vol 118 (2) ◽  
pp. 141-146 ◽  
Author(s):  
S. Abrate
Keyword(s):  
Natural Frequency ◽  
Material Properties ◽  
Composite Structures ◽  
Natural Frequencies ◽  
Ritz Method ◽  
Laminated Composite ◽  
Composite Plates ◽  
Mode Shapes ◽  
Fundamental Natural Frequency ◽  
Wide Range

While many advances were made in the analysis of composite structures, it is generally recognized that the design of composite structures must be studied further in order to take full advantage of the mechanical properties of these materials. This study is concerned with maximizing the fundamental natural frequency of triangular, symmetrically laminated composite plates. The natural frequencies and mode shapes of composite plates of general triangular planform are determined using the Rayleigh-Ritz method. The plate constitutive equations are written in terms of stiffness invariants and nondimensional lamination parameters. Point supports are introduced in the formulation using the method of Lagrange multipliers. This formulation allows studying the free vibration of a wide range of triangular composite plates with any support condition along the edges and point supports. The boundary conditions are enforced at a number of points along the boundary. The effects of geometry, material properties and lamination on the natural frequencies of the plate are investigated. With this stiffness invariant formulation, the effects of lamination are described by a finite number of parameters regardless of the number of plies in the laminate. We then determine the lay-up that will maximize the fundamental natural frequency of the plate. It is shown that the optimum design is relatively insensitive to the material properties for the commonly used material systems. Results are presented for several cases.

SHEAR BUCKLING OF CORRUGATED PLATES WITH EDGES ELASTICALLY RESTRAINED AGAINST ROTATION

2004 ◽  
Vol 04 (01) ◽  
pp. 89-104 ◽  
Author(s):  
CHAWALIT MACHIMDAMRONG ◽  
EIICHI WATANABE ◽  
TOMOAKI UTSUNOMIYA
Keyword(s):  
Ritz Method ◽  
Transition Curve ◽  
Mindlin Plate ◽  
Box Girders ◽  
Plate Buckling ◽  
Rotational Restraint ◽  
Simple Support ◽  
Shear Buckling ◽  
Corrugated Plates ◽  
Elastically Restrained

This paper presents an estimation of the elastic shear buckling capacity of corrugated plates with edges elastically restrained against rotation. The corrugated plate possesses higher shear buckling capacity compared to an unfolded flat plate. It has been used to replace the concrete web in PC box girders in recent bridge constructions in Japan. In this study, the corrugated plate is modelled as an orthotropic Mindlin plate. Elastically rotational restraint on boundary edges is taken into account in the form of rotational springs in the analysis. The prediction of buckling capacities of corrugated plates is carried out by using the Rayleigh–Ritz method, which was proved to be consistent with those as predicted by existing formulas for the limiting cases of simply-supported and clamped edges. The present study covers the more general case of elastically rotational restraint on the boundary edges showing transition curve of plate buckling capacities from the case of simple support to the case of clamped support.

BUCKLING OF A PLATE ON A PASTERNAK FOUNDATION UNDER UNIFORM IN-PLANE BENDING LOADS

2013 ◽  
Vol 13 (03) ◽  
pp. 1250070 ◽  
Author(s):  
CASEY R. BRISCOE ◽  
SUSAN C. MANTELL ◽  
JANE H. DAVIDSON
Keyword(s):  
Local Buckling ◽  
Sandwich Panels ◽  
Core Material ◽  
Load Parameter ◽  
Buckling Strength ◽  
Thin Walled Structures ◽  
Special Cases ◽  
Order Of Magnitude ◽  
Bending Loads ◽  
Plane Bending

In-plane bending loads occur in many thin-walled structures, including web core sandwich panels (foam-filled panels with interior webs) under transverse loading. The design of such structures is limited in part by local buckling of the thin webs and the subsequent impact on stiffness and strength. However, the core material can have a significant impact on web buckling strength and thus must be considered in design. This paper presents solutions for the buckling strength of simply supported plates under in-plane bending loads. The location of the neutral bending axis is allowed to vary and is characterized by a load parameter. A Pasternak model is used to account for the resistance of the foundation to compression and shear. Using the principle of minimum potential energy, buckling solutions are developed for infinitely long plates and representative foundation materials. The solutions match known results for two special cases: Uniform loading with variable foundation, and bending loads with no foundation. An order of magnitude increase in buckling strength is possible, depending on loading and foundation stiffness. The results suggest an important avenue for future development of lightweight structures, including sandwich panels and structures such as plate girders that are not typically associated with the use of foam filling.

Elastic Web Buckling Strength of Pultruded Flexural Members

2004 ◽  
Vol 261-263 ◽  
pp. 621-626 ◽  
Author(s):  
Soon Jong Yoon ◽  
Jae Ho Jung ◽  
Won Sup Jang
Keyword(s):  
Orthotropic Plate ◽  
Numerical Technique ◽  
Ritz Method ◽  
Local Buckling ◽  
Composite Plates ◽  
Buckling Strength ◽  
Simply Supported ◽  
Web Buckling ◽  
Buckling Coefficient ◽  
The Web

This paper presents the analytical investigations pertaining to the elastic buckling behavior of orthotropic composite plates. By the pultrusion process the structural shapes composed of orthotropic plate components are readily available in the construction market. When the member is utilized for the flexure, lateral-torsional buckling and local buckling behaviors must be taken into consideration. In the local buckling analysis, flange and web local buckling analyses must be conducted in the design of such a member. For finding the web buckling strength, the buckling equation for the orthotropic plate under linearly distributed in-plane forces is derived by using the Rayleigh-Ritz method. The boundary conditions of plate are assumed that the loaded edges are simply supported and the unloaded edges are simply supported or fixedly supported. The buckling coefficient of a plate having different orthogonal mechanical properties is found by using the numerical technique and the minimum buckling coefficient is suggested. In addition, simplified form of equation for predicting the minimum buckling coefficient for the plate is proposed. Brief discussion on the design criteria relating to the web local buckling is also provided.

Electroelastic modeling of thin-laminated composite plates with surface-bonded piezo-patches using Rayleigh–Ritz method

2018 ◽  
Vol 29 (10) ◽  
pp. 2192-2205 ◽  
Author(s):  
Mehmet Murat Gozum ◽  
Amirreza Aghakhani ◽  
Gokhan Serhat ◽  
Ipek Basdogan
Keyword(s):  
Modal Analysis ◽  
Vibration Analysis ◽  
Composite Structures ◽  
Ritz Method ◽  
Laminated Composite ◽  
Composite Plates ◽  
System Level ◽  
Laminated Composite Plates ◽  
Modeling Tools ◽  
Analysis And Design

Laminated composite panels are extensively used in various engineering applications. Piezoelectric transducers can be integrated into such composite structures for a variety of vibration control and energy harvesting applications. Analyzing the structural dynamics of such electromechanical systems requires precise modeling tools which properly consider the coupling between the piezoelectric elements and the laminates. Although previous analytical models in the literature cover vibration analysis of laminated composite plates with fully covered piezoelectric layers, they do not provide a formulation for modeling the piezoelectric patches that partially cover the plate surface. In this study, a methodology for vibration analysis of laminated composite plates with surface-bonded piezo-patches is developed. Rayleigh–Ritz method is used for solving the modal analysis and obtaining the frequency response functions. The developed model includes mass and stiffness contribution of the piezo-patches as well as the two-way electromechanical coupling effect. Moreover, an accelerated method is developed for reducing the computation time of the modal analysis solution. For validations, system-level finite element simulations are performed in ANSYS software. The results show that the developed analytical model can be utilized for accurate and efficient analysis and design of laminated composite plates with surface-bonded piezo-patches.

scholarly journals Introduction to Macroscopic Optimal Design in the Mechanics of Composite Materials and Structures

2021 ◽  
Vol 5 (2) ◽  
pp. 36
Author(s):  
Aleksander Muc
Keyword(s):  
Composite Materials ◽  
Composite Structures ◽  
Constitutive Relations ◽  
A Priori ◽  
Chemical Properties ◽  
Composite Plates ◽  
Failure Criteria ◽  
Lagrange Equations ◽  
Homogenization Methods ◽  
Mechanics Of Composite Materials

The main goal of building composite materials and structures is to provide appropriate a priori controlled physico-chemical properties. For this purpose, a strengthening is introduced that can bear loads higher than those borne by isotropic materials, improve creep resistance, etc. Composite materials can be designed in a different fashion to meet specific properties requirements.Nevertheless, it is necessary to be careful about the orientation, placement and sizes of different types of reinforcement. These issues should be solved by optimization, which, however, requires the construction of appropriate models. In the present paper we intend to discuss formulations of kinematic and constitutive relations and the possible application of homogenization methods. Then, 2D relations for multilayered composite plates and cylindrical shells are derived with the use of the Euler–Lagrange equations, through the application of the symbolic package Mathematica. The introduced form of the First-Ply-Failure criteria demonstrates the non-uniqueness in solutions and complications in searching for the global macroscopic optimal solutions. The information presented to readers is enriched by adding selected review papers, surveys and monographs in the area of composite structures.

scholarly journals The Effect of Void Arrangement on the Pattern Transformation of Porous Soft Solids under Biaxial Loading

Materials ◽  
2021 ◽  
Vol 14 (5) ◽  
pp. 1205
Author(s):  
Hai Qiu ◽  
Ying Li ◽  
Tianfu Guo ◽  
Shan Tang ◽  
Zhaoqian Xie ◽  
...  
Keyword(s):  
Biaxial Loading ◽  
Tensile Deformation ◽  
Biaxial Stress ◽  
Porous Solids ◽  
Biaxial Compression ◽  
Structural Topology ◽  
Soft Solids ◽  
Tension And Compression ◽  
Inclined Angle ◽  
Pattern Transformation

Structural topology and loading condition have important influences on the mechanical behaviors of porous soft solids. The porous solids are usually set to be under uniaxial tension or compression. Only a few studies have considered the biaxial loads, especially the combined loads of tension and compression. In this study, porous soft solids with oblique and square lattices of circular voids under biaxial loadings were studied through integrated experiments and numerical simulations. For the soft solids with oblique lattices of circular voids, we found a new pattern transformation under biaxial compression, which has alternating elliptic voids with an inclined angle. This kind of pattern transformation is rarely reported under uniaxial compression. Introducing tensile deformation in one direction can hamper this kind of pattern transformation under biaxial loading. For the soft solids with square lattices of voids, the number of voids cannot change their deformation behaviors qualitatively, but quantitatively. In general, our present results demonstrate that void morphology and biaxial loading can be harnessed to tune the pattern transformations of porous soft solids under large deformation. This discovery offers a new avenue for designing the void morphology of soft solids for controlling their deformation patterns under a specific biaxial stress-state.

Strength Loss in Composite Cylinders Under Impact

1988 ◽  
Vol 110 (2) ◽  
pp. 180-184 ◽  
Author(s):  
A. P. Christoforou ◽  
S. R. Swanson
Keyword(s):  
Composite Structures ◽  
Composite Plates ◽  
Strength Loss ◽  
Pressure Vessels ◽  
Fourier Series Expansion ◽  
Lateral Impact ◽  
Low Velocity ◽  
Expansion Procedure ◽  
The Impact ◽  
Composite Cylinders

The problem of strength loss in composite structures due to impact appears to be important due to the sensitivity of advanced composites to these loadings. Although a number of studies have been carried out on impact of flat composite plates, relatively little work has been done on tubular geometries such as pressure vessels despite the usage in applications. We have addressed the problem of calculating strength loss due to low velocity, lateral impact of composite cylinders. In our model we use an existing Fourier Series expansion procedure to calculate ply stresses and strains, compare these values with allowables to predict fiber breakage during the impact, and finally use fracture mechanics to predict the strength loss due to the impact. Although the model is quite simplified, the general trends of experiments appear to be represented.

Edge Illumination X-Ray Phase Contrast Imaging and Ultrasonic Attenuation for Porosity Quantification in Composite Structures

2021 ◽  
Author(s):  
Dana Shoukroun ◽  
Sandro Olivo ◽  
Paul Fromme
Keyword(s):  
Carbon Fiber ◽  
Composite Structures ◽  
Phase Contrast ◽  
Ultrasonic Attenuation ◽  
Aerospace Industry ◽  
Composite Plates ◽  
Phase Contrast Imaging ◽  
Fiber Reinforced ◽  
Contrast Imaging ◽  
X Ray

Abstract Carbon fiber reinforced composites are widely used in the aerospace industry, due to their low weight and high strength. Porosity often occurs during the manufacturing of composite structures, which can compromise the structural integrity of the part and affect its mechanical properties. In the aerospace industry a typical requirement for structural components is for the porosity content to be kept below 2%. Non-destructive evaluation (NDE) techniques are used to estimate the porosity content in composite components, the most common being ultrasonic attenuation and X-ray computed tomography (CT). Planar Edge Illumination X-ray Phase Contrast Imaging (EI XPCI) was used to quantify the porosity content in woven carbon fiber reinforced composite plates with porosity ranging between 0.7% and 10.7%. A new metric was introduced, the standard deviation of the differential phase (STDVDP) signal, which represents the variation of inhomogeneity in the plates for features of a scale equal to or above the system resolution (here 12μm). The SDTVDP was found to have a very high correlation with porosity content estimated from matrix digestion and ultrasonic attenuation, hence providing a promising new methodology to quantify porosity in composite plates.

Stresses and Displacements in a Rotating Conical Shell

1943 ◽  
Vol 10 (2) ◽  
pp. A53-A61
Author(s):  
J. L. Meriam
Keyword(s):  
Conical Shell ◽  
Body Force ◽  
Theory Of Elasticity ◽  
Common Type ◽  
The Body ◽  
Surface Loading ◽  
Thin Walled Structures ◽  
Special Cases ◽  
Engineering Problems ◽  
Rotating Conical Shell

Abstract The analysis of shells is an important subdivision of the general theory of elasticity, and its application is useful in the solution of engineering problems involving thin-walled structures. A common type of shell is one which possesses symmetry with respect to an axis of revolution. A theory for such shells has been developed by various investigators (1, 2, 3, 6) and applied to a few simple cases such as the cylindrical, spherical, and conical shapes. Boundary conditions, for the most part, have been simple static ones, and conditions of surface loading have been included in certain special cases. This paper extends the theory of axially symmetrical shells by including the body force of rotation about the axis and applies the results to the rotating conical shell. The analysis follows a pattern established by several investigators (1, 2, 3, 6) and for this reason is abbreviated to a considerable extent. Only where the inclusion of the body force makes elucidation advisable or where a slightly different method of approach is used are the steps presented in more detail.

Sign in / Sign up

Export Citation Format

Share Document