1988 Vol. 5, No. 2
1988, 5(2): 1-Ⅰ.
Abstract:
In this paper, the problem of plane waves in a thin-walled tube of orthotropic composite under combined actions of extension and torsion are investigated by using the method of characteristics. The wave speeds, the characteristic relations and the general solution of the problem are obtained and a special initial-boundary value problem is solved.The simple wave solutions are also obtained and discussed in detail.The results show that there exist a number of characteristic properties and physical phenomena which differ substantially from those of waves in an isotropic medium. For example, there are two waves in the thin-walled tube of composite, and one can classify them as fast wave and slow wave according to their wave speeds.Each wave is neither extensional nor torsional, but rather a combination of both, Here the extension and torsion are tightly couppled.Hence, a general end loading will produces both waves, not just one of them.
In this paper, the problem of plane waves in a thin-walled tube of orthotropic composite under combined actions of extension and torsion are investigated by using the method of characteristics. The wave speeds, the characteristic relations and the general solution of the problem are obtained and a special initial-boundary value problem is solved.The simple wave solutions are also obtained and discussed in detail.The results show that there exist a number of characteristic properties and physical phenomena which differ substantially from those of waves in an isotropic medium. For example, there are two waves in the thin-walled tube of composite, and one can classify them as fast wave and slow wave according to their wave speeds.Each wave is neither extensional nor torsional, but rather a combination of both, Here the extension and torsion are tightly couppled.Hence, a general end loading will produces both waves, not just one of them.
1988, 5(2): 11-Ⅱ.
Abstract:
An analytical investigation of the large deflection behaviour of rectilinear orthotropic circular plates under uniform means of analyzing the flexural stiffness of the plate, a non-axisymrnetrical flexural deflection is founded. Galerkin's procedure is used to solve one of the von Karmantype large deflection equations and an exact solution is obtained for the rest equation.The solution to the plates with three kinds of orthotropies, Glass/EPoxy, Boron/Epoxy and Graphite/Epoxy, is found under the clamping, radially immovable boundary conditions.The influence of the non-axisymmetrical def leation is investigated. The results show as follows.
An analytical investigation of the large deflection behaviour of rectilinear orthotropic circular plates under uniform means of analyzing the flexural stiffness of the plate, a non-axisymrnetrical flexural deflection is founded. Galerkin's procedure is used to solve one of the von Karmantype large deflection equations and an exact solution is obtained for the rest equation.The solution to the plates with three kinds of orthotropies, Glass/EPoxy, Boron/Epoxy and Graphite/Epoxy, is found under the clamping, radially immovable boundary conditions.The influence of the non-axisymmetrical def leation is investigated. The results show as follows.
1988, 5(2): 17-Ⅲ.
Abstract:
This paper presents studies of the interlaminar stresses of a N-layer laminated composite bar loaded by end forces.At first, the interlaminar stresses are expressed as following series forms.
This paper presents studies of the interlaminar stresses of a N-layer laminated composite bar loaded by end forces.At first, the interlaminar stresses are expressed as following series forms.
1988, 5(2): 28-Ⅳ.
Abstract:
In Ref (1) the authors of this paper put forward a elastic pin model consideringre deformation of pin and the effects of friction in contact area On the basis of above work, this paper studied the stresses around a pinloaded hole in finite laminate First, the flexibility equation of pin and the analytical expression of equivalent nodel forces around the hole have been established.Next, based on the contact conditions, and using the analytical formulas mentioned above and FEM, the FEM-anatytical mixed method is developed for calculating the stresses around a pin-loaded hole in finite laminate.Finally, a numerical example is given.The analysis shows that the results of the calculation are verp consistant with the experimental data.
In Ref (1) the authors of this paper put forward a elastic pin model consideringre deformation of pin and the effects of friction in contact area On the basis of above work, this paper studied the stresses around a pinloaded hole in finite laminate First, the flexibility equation of pin and the analytical expression of equivalent nodel forces around the hole have been established.Next, based on the contact conditions, and using the analytical formulas mentioned above and FEM, the FEM-anatytical mixed method is developed for calculating the stresses around a pin-loaded hole in finite laminate.Finally, a numerical example is given.The analysis shows that the results of the calculation are verp consistant with the experimental data.
1988, 5(2): 37-Ⅴ.
Abstract:
On the basis of Ref [1, 2] in this paper, we investigate the nonlinear elastic buckline problem of orthotropic laminated cylindrical panels under the action of axial load.The nonlinear constitutme relations of more ana matrix are considered. Cross-plied and ±θ angle-plied cases are discussed. The small elastic-plastic deformation theory and the law of mixture of tomposite materials and the linear theory of stability are used. The formulas for the critical loads of nonlinear elastic buckling are obtained.The method of determining the constants of material Property from some simple experiments.Numerical examples and discussions are given. The experimental methods to measure the nonlinear elastic constants of unidirectional composite lamina are given in the appendix. Only the theoretical research is done in phis paper.It is a regret that we have not suitable condition to do experimental work. But the method given in this paper is valuable to the engineers and researchers.
On the basis of Ref [1, 2] in this paper, we investigate the nonlinear elastic buckline problem of orthotropic laminated cylindrical panels under the action of axial load.The nonlinear constitutme relations of more ana matrix are considered. Cross-plied and ±θ angle-plied cases are discussed. The small elastic-plastic deformation theory and the law of mixture of tomposite materials and the linear theory of stability are used. The formulas for the critical loads of nonlinear elastic buckling are obtained.The method of determining the constants of material Property from some simple experiments.Numerical examples and discussions are given. The experimental methods to measure the nonlinear elastic constants of unidirectional composite lamina are given in the appendix. Only the theoretical research is done in phis paper.It is a regret that we have not suitable condition to do experimental work. But the method given in this paper is valuable to the engineers and researchers.
1988, 5(2): 46-Ⅴ.
Abstract:
The classical methods for estimating from samples the unknown parameters in the distribution function are the moment method and the maximum likelihood method.However, these methods are not always effective when they are used to estimate the three unknown parameters.In this paper, for the sake of estimating the three parameters of the modified Weibull distribution function proposed previously, the existing graphical estimation method has been modified, and the united-estimation method has been suggested in addition.The modified graphical method does not need to use the special probability-paper, nor does it need to trace points over and over again. The united method is a combination of the moment estimation and the maximum likelihood estimation.By estimating the parameters of a vast amount of random samples, it has been shown that the united method is more effective than the standardized variate estimation method proposed by Talreja recently.
The classical methods for estimating from samples the unknown parameters in the distribution function are the moment method and the maximum likelihood method.However, these methods are not always effective when they are used to estimate the three unknown parameters.In this paper, for the sake of estimating the three parameters of the modified Weibull distribution function proposed previously, the existing graphical estimation method has been modified, and the united-estimation method has been suggested in addition.The modified graphical method does not need to use the special probability-paper, nor does it need to trace points over and over again. The united method is a combination of the moment estimation and the maximum likelihood estimation.By estimating the parameters of a vast amount of random samples, it has been shown that the united method is more effective than the standardized variate estimation method proposed by Talreja recently.
1988, 5(2): 54-Ⅵ.
Abstract:
A bundle of fibers apd it's composite may be considered as a parallel structure.The strength of a parallel structure can be predicted from the strength of its component elements.In this paper, a semi-empirical statistical representation for the parallel model has Been proposed.This, expression is chosen in the same form as the function for the probability strength of the component elements, and is quite convenient for calculation.The statistical strengths of the glass fiber bunches and the glass/epoxy (0/90)s laminates have been investigated.experimentally.The experimental results are compared with the predicted results obtained by applying the parallel model and good agreement between them has been found in general.The empirical constant contained in the expraasion is concerned wrth the property and stacling sequence of the component elements as well as the integrated form and processing technology of the parallel structure, and their influence on it remains to be investigated and further studied.
A bundle of fibers apd it's composite may be considered as a parallel structure.The strength of a parallel structure can be predicted from the strength of its component elements.In this paper, a semi-empirical statistical representation for the parallel model has Been proposed.This, expression is chosen in the same form as the function for the probability strength of the component elements, and is quite convenient for calculation.The statistical strengths of the glass fiber bunches and the glass/epoxy (0/90)s laminates have been investigated.experimentally.The experimental results are compared with the predicted results obtained by applying the parallel model and good agreement between them has been found in general.The empirical constant contained in the expraasion is concerned wrth the property and stacling sequence of the component elements as well as the integrated form and processing technology of the parallel structure, and their influence on it remains to be investigated and further studied.
1988, 5(2): 59-Ⅶ.
Abstract:
In this paper, the expansions of displacements and stresses of a plate with an edge crack are derived, according to the theary of anisotropic elasticity and the boundary conditions on tha crack surfacesa on the basis of above analysis, the stress intensity factors of orthotropic plates with central cracks, double edge cracks and nesa-hole cracks are calculated by means of generalized variational method.The convargenci}s of the computational resuits are satisfactorily well for all of the cases mentioned above.Finally, the reaults for isotropic cases agree with those of Ref (8) nicely.
In this paper, the expansions of displacements and stresses of a plate with an edge crack are derived, according to the theary of anisotropic elasticity and the boundary conditions on tha crack surfacesa on the basis of above analysis, the stress intensity factors of orthotropic plates with central cracks, double edge cracks and nesa-hole cracks are calculated by means of generalized variational method.The convargenci}s of the computational resuits are satisfactorily well for all of the cases mentioned above.Finally, the reaults for isotropic cases agree with those of Ref (8) nicely.
1988, 5(2): 67-Ⅷ.
Abstract:
The purpose of the present study is to predict the thermal stress including interlaminar stress near the free region for axisymmetric revolution lamina, ted composite shell structure under hydrothermal service loading condition.Two aspects of thermal interlaminar stress analysis for laminated compolite shells are presented in this paper.First, the formulas of two kinds of quasi-3D isoparametric quadrilateral elements bused on anisotropic heat conduction theory and thermoelasticity are developed and can be used to study temperature field distribution and it's corrosponding thermal stress field for laminated composite shells.Secondly, we concern with the effects of stacking sequence, laminated orientation, uniformity of temperature field and the ratio of shall thickness to curvature radial upon the delamination along the interface of the shells.Tha numerical results have shown the following conclusions.
The purpose of the present study is to predict the thermal stress including interlaminar stress near the free region for axisymmetric revolution lamina, ted composite shell structure under hydrothermal service loading condition.Two aspects of thermal interlaminar stress analysis for laminated compolite shells are presented in this paper.First, the formulas of two kinds of quasi-3D isoparametric quadrilateral elements bused on anisotropic heat conduction theory and thermoelasticity are developed and can be used to study temperature field distribution and it's corrosponding thermal stress field for laminated composite shells.Secondly, we concern with the effects of stacking sequence, laminated orientation, uniformity of temperature field and the ratio of shall thickness to curvature radial upon the delamination along the interface of the shells.Tha numerical results have shown the following conclusions.
1988, 5(2): 75-Ⅸ.
Abstract:
With the advent of the widespread use of fiber-reinforced composite materials, the natural frequencies and mode shapes of laminated plates has been widened int, rest, However, there are stretching-bending and bending-twisting coupling-as well as shear deformation in laminated plates due to the orientation of the plies and stacking sequence, so it is difficult to get anaolytical solutions of many dynamic problems in engineering.Therefore, a numerical method of both simplicity and accuracy must be sought to meet the needs for engineering counting.
With the advent of the widespread use of fiber-reinforced composite materials, the natural frequencies and mode shapes of laminated plates has been widened int, rest, However, there are stretching-bending and bending-twisting coupling-as well as shear deformation in laminated plates due to the orientation of the plies and stacking sequence, so it is difficult to get anaolytical solutions of many dynamic problems in engineering.Therefore, a numerical method of both simplicity and accuracy must be sought to meet the needs for engineering counting.
1988, 5(2): 81-Ⅸ.
Abstract:
Based on Timoshenko's beam theory, the governing equations and boundary conditions of static and dynamic analysis of laminated beams, which can be reduced to the equations of Timoshenko beam in the cass of single layer, are established in this paper by using effective stiffness method and Hamilton's principle, and the analytic solution and numerical results of some problems of laminated beams are obtained by employing the governing equations.
Based on Timoshenko's beam theory, the governing equations and boundary conditions of static and dynamic analysis of laminated beams, which can be reduced to the equations of Timoshenko beam in the cass of single layer, are established in this paper by using effective stiffness method and Hamilton's principle, and the analytic solution and numerical results of some problems of laminated beams are obtained by employing the governing equations.
1988, 5(2): 89-Ⅹ.
Abstract:
The analysis of the room temperature shape of asymmetrical laminates after high temperature curing is an important item for designing and manufaeturing of composite materials.It has been shown that some unsynimetric laminates have cylindrical room temperature shapes.In addition, some unsynimetric laminates exhibit two stable foom temperature configurations, both cylindrical.This paper presents a simple formula for roorn.temperature shape of unsymmetric cross-ply laminates.The theory is based on the extension of classical lamination theory which accounts for geometric nonlinearity.The large displacements of thin plate is then derived.The.formula for calculating the deformed curvature and inplane strains, deflections and inplane displacmenu are accurately agree with the existing experimental data.
The analysis of the room temperature shape of asymmetrical laminates after high temperature curing is an important item for designing and manufaeturing of composite materials.It has been shown that some unsynimetric laminates have cylindrical room temperature shapes.In addition, some unsynimetric laminates exhibit two stable foom temperature configurations, both cylindrical.This paper presents a simple formula for roorn.temperature shape of unsymmetric cross-ply laminates.The theory is based on the extension of classical lamination theory which accounts for geometric nonlinearity.The large displacements of thin plate is then derived.The.formula for calculating the deformed curvature and inplane strains, deflections and inplane displacmenu are accurately agree with the existing experimental data.
1988, 5(2): 93-Ⅺ.
Abstract:
In this paper a new metkod referred to as objective speckle of sticking foil. has been employed in order to deterrizine strain distribution in a carbon fiber composite box beam.The specimen surface was treated by relative easy techniques.Three fullfield contour maps are obtained with clear lines of equal displacemet in 0°, 90°, and 45° directions, respectively.The experiment was carried out in an ordinary labor atory without a dark room or a vibration isolation bench.The results are agreed well with those by calculation according to the theory of engineering bea ms and by measuring of electrical-resistance strain gages.
In this paper a new metkod referred to as objective speckle of sticking foil. has been employed in order to deterrizine strain distribution in a carbon fiber composite box beam.The specimen surface was treated by relative easy techniques.Three fullfield contour maps are obtained with clear lines of equal displacemet in 0°, 90°, and 45° directions, respectively.The experiment was carried out in an ordinary labor atory without a dark room or a vibration isolation bench.The results are agreed well with those by calculation according to the theory of engineering bea ms and by measuring of electrical-resistance strain gages.
1988, 5(2): 97-Ⅺ.
Abstract:
A theory of bending for the symmetrical laminated plates is derived. The distribution of transverse shear stresses is assumed and then the model of displacements is developed. By solving the governing equations in terms of displacement components, we can get dispalacements and stresses for a symmetrically laminated orthotropic plates.Numerical examples show good accuracy of the approach presented by comparing the results from the exact theory of elasticity.
A theory of bending for the symmetrical laminated plates is derived. The distribution of transverse shear stresses is assumed and then the model of displacements is developed. By solving the governing equations in terms of displacement components, we can get dispalacements and stresses for a symmetrically laminated orthotropic plates.Numerical examples show good accuracy of the approach presented by comparing the results from the exact theory of elasticity.
