Analytic solution of angle-ply laminated plates under extension, bending, and torsion

2019 ◽  
Vol 54 (8) ◽  
pp. 1093-1106
Author(s):  
Shen-Haw Ju ◽  
Wen-Yu Liang ◽  
Hsin-Hsiang Hsu ◽  
Jiann-Quo Tarn
Keyword(s):  
Numerical Solutions ◽  
Anisotropic Elasticity ◽  
Laminated Plates ◽  
Rectangular Section ◽  
State Space Approach ◽  
Present Solution ◽  
End Conditions ◽  
Combined Action ◽  
Space Approach

This paper develops a Hamiltonian state space approach for analytic determination of deformation and stress fields in multilayered monoclinic angle-ply laminates under the combined action of extension, bending, and torsion. The present solution satisfies the equations of anisotropic elasticity, the end conditions, the traction-free boundary conditions on the four edge surfaces of the rectangular section, and the interfacial continuity conditions in multilayered laminates. The proposed method only requires the solutions of matrix and eigen equations, regardless of the number or lamination of the layers. The finite element analyses are used to validate the accuracy of the analysis. The analytical solution and the numerical solutions are in excellent agreement.

Exact Analysis of Stress Fields in Composite Laminates under Extension

2014 ◽  
Vol 30 (5) ◽  
pp. 477-489 ◽  
Author(s):  
W.-Y. Liang ◽  
W.-D. Tseng ◽  
J.-Q. Tarn
Keyword(s):  
State Space ◽  
Composite Laminates ◽  
Complete Solution ◽  
Rectangular Section ◽  
State Space Approach ◽  
Exact Analysis ◽  
End Conditions ◽  
Particular Solution ◽  
Uniform Extension ◽  
Space Approach

AbstractExact analysis of displacements and stresses in 2-D orthotopic laminates under extension is conducted. On the basis of the Hamiltonian state space approach and the transfer matrix method, a complete solution, in the context of generalized strain, which exactly satisfies the state space equation, the traction-free BC on the top and bottom surfaces of the rectangular section, the interfacial continuity conditions in multi-layered laminates, and the end conditions on free edges, is obtained by combing the eigensolutions and the particular solution. Evaluating of the stresses in the boundary layer for verification shows that the stress decay in laminates under uniform extension may be slow and the edge effects may be pronounced.

scholarly journals State space approach with FEM for the determination of structural behaviour of composite plates

2017 ◽  
Vol 8 (4) ◽  
pp. 468-483
Author(s):  
Asad Shukri Albostami ◽  
Zhangjian Wu ◽  
Zhenmin Zou
Keyword(s):  
Plate Thickness ◽  
Composite Plates ◽  
Thickness Direction ◽  
Middle Plane ◽  
Structural Behaviour ◽  
State Space Approach ◽  
Content Type ◽  
Simply Supported ◽  
Space Approach

Purpose An analytical investigation has been carried out for a simply supported rectangular plate with two different loading conditions by using 3D state space approach (SSA). Also, the accurate location of the neutral plane (N.P.) through the thickness of the plate can be identified: the N.P. is shifted away from the middle plane according to the loading condition. The paper aims to discuss these issues. Design/methodology/approach SSA and finite element method are used for the determination of structural behaviour of simply supported orthotropic composite plates under different types of loading. The numerical results from a finite element model developed in ABAQUS. Findings The effect of the plate thickness on displacements and stresses is described quantitatively. It is found that the N.P. of the plate, identified according to the values of the in-plane stresses through the thickness direction, is shifted away from the middle plane. Further investigation shows that the position of the N.P. is loading dependant. Originality/value This paper describe the effect of the plate thickness on displacements and stresses quantitatively by using an exact solution called SSA. Also, it is found that the N.P. of the plate, identified according to the values of the in-plane stresses through the thickness direction, is shifted away from the middle plane. Further investigation shows that the position of the N.P. is loading dependant.

Analysis of Multiholed Orthotropic Laminated Plates by the Boundary-Point-Least-Squares Method

1975 ◽  
Vol 97 (2) ◽  
pp. 118-122 ◽  
Author(s):  
S. G. Sampath ◽  
L. E. Hulbert
Keyword(s):  
Least Squares ◽  
Boundary Point ◽  
Numerical Solutions ◽  
Least Squares Method ◽  
Elliptical Hole ◽  
Laminated Plates ◽  
Series Solutions ◽  
Orthotropic Plates ◽  
Multiply Connected

The paper describes the application of boundary-point-least-squares method (BPLS) for the determination of stresses in multiply connected finite orthotropic plates under plane stress. Series solutions composed of mapping functions are employed. Numerical solutions presented include the case of an orthotropic plate with an elliptical hole with orientation noncoincident with the material axes.

Approximate Determination of Eigen-Values of Classically Damped System with Added Viscous Damper

2016 ◽  
Vol 821 ◽  
pp. 221-228 ◽  
Author(s):  
Stanislav Hračov
Keyword(s):  
Perturbation Technique ◽  
Approximate Determination ◽  
Viscous Damper ◽  
State Space Approach ◽  
Damped System ◽  
Eigen Values ◽  
The Difference ◽  
Damped Systems ◽  
Space Approach

In this paper, an approximate method for determining the complex eigen-values of non-classically damped linear system is presented. Only the systems consisting of a linear classically damped system to which one viscous damper is attached are assumed. The proposed method reflects the difference in the eigen-values of classically and non-classically damped systems using the first-order perturbation technique. The procedure is easy to code and avoids using a numerically demanding state-space approach. It operates in the original dimension of the physical problem and requires only the knowledge of eigen-modes and eigen-values of the classically damped and undamped systems. Numerical example is given to demonstrate application and accuracy of the method.

The Effect of Stress and Warfarin on the Adrenal Gland in Relation to Spontaneous Hemorrhage, as Judged by Measurement of Adrenal Ascorbic Acid and Serum Corticosterone

1971 ◽  
Vol 26 (02) ◽  
pp. 275-288 ◽  
Author(s):  
S Chattopadhyay ◽  
D. D Johnson ◽  
G. J Millar ◽  
L. B Jaques
Keyword(s):  
Ascorbic Acid ◽  
Acid Concentration ◽  
Ascorbic Acid Concentration ◽  
Corticosterone Concentration ◽  
Serum Corticosterone ◽  
Spontaneous Hemorrhage ◽  
Combined Action ◽  
Series Of Experiments ◽  
Pituitary Adrenal Axis

SummaryRats were subjected to the following procedures: No treatment, Stressor (10% NaCl i.p.), Warfarin for 7 days, Stressor followed by Warfarin; and groups were sacrificed at intervals for assessment of spontaneous hemorrhage and of adrenal ascorbic acid concentration. There was no hemorrhage in the no treatment and stressor groups; some hemorrhage in the warfarin group; profound hemorrhage with Warfarin + Stressor. The adrenal ascorbic acid concentration was found to be lower, 8 h and again 5 days after stress, and remained lower in the warfarin + stress animals. Warfarin had no effect on adrenal ascorbic acid level.In another series of experiments in which the stress consisted of an electric current to the cage floor for 6 sec over 15 min, rats were sacrificed daily for determination of serum corticosterone concentration and occurrence of spontaneous hemorrhage. There was a statistically significant increase of serum corticosterone concentration with stress, warfarin and combined warfarin and stress treatments (P< 0.001 for all three variables). There was a significant correlation (r = 0.96 and 0.89, P< 0.01) for serum corticosterone concentration with hemorrhage score and incidence of hemorrhage in stressed rats receiving warfarin, but not in those receiving only warfarin. The results indicate an activation, rather than an exhaustion, of the pituitary-adrenal axis during the combined action of anticoagulant and stress, which results in the development of spontaneous hemorrhage.

A novel method for the determination of linting propensity of paper

TAPPI Journal ◽  
2012 ◽  
Vol 11 (10) ◽  
pp. 9-17
Author(s):  
ALESSANDRA GERLI ◽  
LEENDERT C. EIGENBROOD
Keyword(s):  
Ash Content ◽  
The Novel ◽  
Offset Printing ◽  
Excellent Correlation ◽  
End Conditions ◽  
Bottom Side ◽  
Novel Method ◽  
Total Fraction

A novel method was developed for the determination of linting propensity of paper based on printing with an IGT printability tester and image analysis of the printed strips. On average, the total fraction of the surface removed as lint during printing is 0.01%-0.1%. This value is lower than those reported in most laboratory printing tests, and more representative of commercial offset printing applications. Newsprint paper produced on a roll/blade former machine was evaluated for linting propensity using the novel method and also printed on a commercial coldset offset press. Laboratory and commercial printing results matched well, showing that linting was higher for the bottom side of paper than for the top side, and that linting could be reduced on both sides by application of a dry-strength additive. In a second case study, varying wet-end conditions were used on a hybrid former machine to produce four paper reels, with the goal of matching the low linting propensity of the paper produced on a machine with gap former configuration. We found that the retention program, by improving fiber fines retention, substantially reduced the linting propensity of the paper produced on the hybrid former machine. The papers were also printed on a commercial coldset offset press. An excellent correlation was found between the total lint area removed from the bottom side of the paper samples during laboratory printing and lint collected on halftone areas of the first upper printing unit after 45000 copies. Finally, the method was applied to determine the linting propensity of highly filled supercalendered paper produced on a hybrid former machine. In this case, the linting propensity of the bottom side of paper correlated with its ash content.

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