Klaus Rohwer

IMPROVED TRANSVERSE SHEAR STRESSES IN COMPOSITE FINITE ELEMENTS BASED ON FIRST ORDER SHEAR DEFORMATION THEORY

A method for calculating improved transverse shear stresses in laminated composite plates, which bases on the first-order shear deformation theory is developed. In contrast to many recently established methods, either higher-order lamination theories or layerwise theories, it is easily applicable to finite elements, since only C0-continuity is necessary and the numerical effort is low. The basic idea is to calculate the transverse shear stresses directly from the transverse shear forces by neglecting the influence of the membrane forces and assuming two cylindrical bending modes. Shear correction factors are no longer required, since the transverse shear stiffnesses are also provided. Numerical examples for symmetric cross-ply and antisymmetric angle-ply laminates show the superiority of the method against using shear correction factors. Furthermore, results obtained with MSC/NASTRAN, which uses a similar but simplified approach, are surpassed.

Higher-order theories for thermal stresses in layered plates

First order shear deformation theory renders quite accurate in-plane stresses even for rather thick plates. By means of equilibrium conditions derivatives of the in-plane stresses can be integrated to determine transverse shear and normal stresses. The need to use in-plane derivatives requires at least cubic shape functions. Simplifying assumptions relieve these requirements leading to the extended 2D method. While under mechanical load this method yields excellent results, poor transverse normal stresses have been obtained for plates under a sinusoidal temperature distribution. This paper traces back these deficiencies to lentil-like deformations of each separate layer. It is proved that third or fifth order displacement approximations through the plate thickness avoid these deficiencies.

Efficient Linear Transverse Normal Stress Analysis of Layered Composite Plates.

Based on the first order shear deformation theory (FSDT) a method is developed for calculating the transverse normal stress (in thickness direction) in layered composite plate structures. Two steps are necessary. First, the transverse shear stress calculation, and second, relying on the results of the first step, the transverse normal stress evaluation. In the first step strain derivatives are substituted with transverse shear forces which in turn are obtained from the corresponding material law. This leads to a derivative-free process which is numerically more accurate than a pure equilibrium approach. As a second step the transverse normal stress is equilibrated to the derivatives of the transverse shear stresses with respect to the in-plane coordinates. As compared to the standard equilibrium approach, the proposed procedure reduces the order of differentiation by one. Thus, only quadratic shape functions are necessary for evaluating the required derivatives on the element level. Numerical examples for symmetric cross-ply and antisymmetric angle-ply laminates show that the exact three-dimensional elasticity solution is very closely approximated. This holds for thin as well as rather thick plates with a slenderness ratio down to five. In contrast to many recently established methods, either higher order lamination theories or layerwise theories, the approach is easily applicable to finite elements, since only C0-continuity is necessary and the numerical effort is low.

Integrated Thermal and Mechanical Analysis of Composite Plates and Shells

Thermal and mechanical analyses of structures are usually performed with non-consistent tools leading to an excessive effort in data adaptation. The application of 2D finite elements for both tasks relaxes this deficiency. With thermal lamination theories assuming a linear or quadratic temperature distribution in the thickness direction, suitable elements are developed and experimentally verified for both steady-state and transient problems. On the basis of a 2D global analysis accurate transverse stresses can be determined from local equilibrium conditions. For laminated plates and cylindrical shells a procedure is presented which allows us to reduce the order of shape functions.

A new strength model for application of a physically based failure criterion to orthogonal 3D fiber reinforced plastics

A strength model for 3D fiber-reinforced plastics consisting of unidirectional layers with a high in-plane fiber density and additional reinforcements perpendicular to the layers with a significantly lower fiber density is presented. The strength model aims to enhance the application range of an existing, physically based failure criterion for inter-fiber fracture of unidirectional fiber-reinforced layers to the above mentioned configuration of 3D-composites. In doing so the fundamental physical basis, the fracture hypothesis of Mohr, and the general mathematical formulation of the criterion are sustained. The enhancement of the application range is achieved by employing a continuous interpolation between the basic strengths of an orthogonal 3D fiber-reinforced layer.

Calculating 3D stresses in layered composite plates and shells

Advanced failure criteria for fiber composites account for all six components of the stress tensor. Plate and shell analysis, however, is sensibly performed by assuming the plane state of stress, which results in global displacements, cross-sectional membrane forces, and bending moments of suitable accuracy. Based on these results, equilibrium conditions can be applied to locally determine the stress components in the transverse direction. Therewith, the transverse shear stresses require first derivatives and transverse normal stresses even second derivatives of the membrane stresses. Higher-order finite elements would be necessary if these stress components are to be determined on the element level. To ease this deficiency, a procedure is proposed based on neglecting the in-plane derivatives of the membrane forces and twisting moments as well as the mixed derivatives of the bending moments. This allows us to reduce the order of differentiation by one. Applicability of this procedure is demonstrated by calculating the transverse shear and normal stresses for layered composite structures of different geometric dimensions and various stacking orders under mechanical as well as thermal loads. Comparison with results from 3D analyses shows excellent accuracy and efficiency of the proposed procedure.

CYCLIC BUCKLING TESTS OF PRE-DAMAGED CFRP STRINGER-STIFFENED PANELS

Experimental results obtained from cyclic buckling and postbuckling tests of pre-damaged stiffened CFRP panels are presented in this paper. This work was conducted within the COCOMAT project funded by the EU with the objective of contributing to the reduction of structural weight at safe design. COCOMAT was targeted at establishing a new design scenario for composite stiffened panels which are understood as part of an aircraft fuselage. This design scenario aimed at exploiting considerable reserves in the load carrying capacity in fiber composite fuselage structures by accurate simulation of collapse. The project results cover an experimental database, improved slow and fast computational tools, as well as design guidelines. A reliable simulation of the collapse load requires taking degradation into account. For the validation of the tools, a sound database of experiments is needed which gives information about the progress of damage during the loading process. In this context, the present paper focuses on the investigation of pre-damaged stringer-stiffened panels under cyclic axial compression. A set of four panels of the same design was split into two variants which differ only in the position of an artificial Teflon disbond beneath a stringer. One panel of each variant was tested statically until collapse in one step as reference, while the other panel was tested cyclically with different amplitudes. Before the test, all test structures were assessed by ultrasonic inspection and the geometric imperfections were measured. During the test, advanced measurement systems such as the ARAMIS system for the measurement of the buckling pattern and thermography for monitoring the skin-stringer separation were utilized in addition to strain gauge measurements and the record of the load shortening data. The test structures, their preparations for testing, the buckling test facility, and the measurement systems used are described. The test results as to the influence of the cyclic loading on the damage progression in the skin-stringer connection are presented and discussed.

Experiments to Detect Damage Progression in Axially Compressed CFRP Panels under Cyclic Loading

The aircraft industry strives for significantly reduced development and operating costs. Reduction of structural weight at safe design is one possibility to reach this objective which is aimed by the running EU project COCOMAT. The main objective of COCOMAT is a future design scenario for composite curved stiffened panels which are understood as parts of real aircraft structures. This design scenario exploits considerable reserve carrying capacities in fibre composite fuselage structures by accurate simulation of collapse. The project results will comprise an experimental data base, improved slow and fast computational tools as well as design guidelines. A reliable simulation of the collapse load requires also taking degradation into account. For the validation of the tools a sound database of experiments are needed which give information about the progress of damage during the loading process. This paper focuses on experimental results of four nominally identical CFRP panels tested within the COCOMAT project at the buckling test facility of the Institute of Composite Structures and Adaptive Systems (DLR). In a first step, three of the four panels were loaded several thousand times. Each time the panel was loaded beyond global buckling and was unloaded to zero. Finally, all panels were tested until collapse. During the tests, advanced measurement systems such as High-Speed-ARAMIS, thermography and Lamb-waves were applied. The test results given in this paper may be used as benchmarks.

Design and Analysis of Composite Panels

European aircraft industry demands for reduced development and operating costs, by 20% and 50% in the short and long term, respectively. Contributions to this aim are provided by the completed project POSICOSS (5thFP) and the running follow-up project COCOMAT (6thFP), both supported by the European Commission. As an important contribution to cost reduction a decrease in structural weight can be reached by exploiting considerable reserves in primary fibre composite fuselage structures through an accurate and reliable simulation of postbuckling up to collapse. The POSICOSS team developed fast procedures for postbuckling analysis of stiffened fibre composite panels, created comprehensive experimental data bases and derived design guidelines. COCOMAT builds up on the POSICOSS results and considers in addition the simulation of collapse by taking degradation into account. The results comprise an extended experimental data base, degradation models, improved certification and design tools as well as design guidelines. The projects POSICOSS and COCOMAT develop improved tools which are validated by experimental results obtained during the projects. Because the new tools must consider a wide range of different aspects a lot of different structures had to be tested. These structures were designed under different design objectives. For the design process the consortium applied already available simulation tools and brought in their own design experience. This paper deals with the design process within both projects and the analysis procedure applied within this task. It focuses on the experience of DLR on the design and analysis of stringer stiffened CFRP panels gained in the frame of these projects.

MODELS AND TOOLS FOR HEAT TRANSFER, THERMAL STRESSES, AND STABILITY OF COMPOSITE AEROSPACE STRUCTURES

An overview of DLRs current research activities and results in the fields of heat transfer, thermal stresses, and thermally induced buckling in composite aerospace structures is given. Novel theories and finite element formulations are presented, realistic modeling of boundary conditions and junction areas is highlighted, experimental validation is discussed, and design guidelines are given.