Rolands Rikards

Analysis for buckling and vibrations of composite stiffened shells and plates

Abstract This paper deals with development of triangular finite element for buckling and vibration analysis of laminated composite stiffened shells. For the laminated shell, an equivalent layer shell theory is employed. The first-order shear deformation theory including extension of the normal line is used. In order to take into account a non-homogeneous distribution of the transverse shear stresses a correction of transverse shear stiffness is employed. Based on the equivalent layer theory with six degrees of freedom (three displacements and three rotations), a finite element that ensures C 0 continuity of the displacement and rotation fields across inter-element boundaries has been developed. Numerical examples are presented to show the accuracy and convergence characteristics of the element. Results of vibration and buckling analysis of stiffened plates and shells are discussed.

Method for identification of elastic properties of laminates based on experiment design

Abstract A numerical-experimental method for the identification of mechanical properties of laminated composites from the experimental results is developed. For the first time it is proposed to use the experiment design to solve the identification (inverse) problems. The basic idea of the proposed approach is that simple mathematical models (response surfaces) are determined only by using the finite element solutions in the reference points of the experiment design. Therefore, a significant reduction (about 50–100 times) in calculations of the identification functional can be achieved in comparison with the conventional methods of minimization. Numerical examples of identification of elastic properties of different laminates from the measured eigenfrequencies of plates are discussed.

Determination of elastic constants of glass/epoxy unidirectional laminates by the vibration testing of plates

Identification of elastic properties of unidirectional glass/epoxy laminates from the measured eigenfrequencies has been performed. The stiffness of the laminates has been investigated by a mixed numerical/experimental method employing the vibration test of plates. Elastic constants of laminates have been determined by using an identification procedure based on experiment design, the finite-element method and the response-surface approach. Elastic properties of laminates with two different fibre-surface treatments have been compared. It was found that only for the transverse elastic modulus is there a statistically significant difference between the composites with good and poor fibre/matrix adhesion.

Surrogate models for optimum design of stiffened composite shells

An optimization procedure is developed for the design of composite stiffened shells subjected to buckling and post-buckling constraints. The optimization method is based on building surrogate models employing the experimental design and response surface methodology. A combined data set consisting of test results of stiffened shells and numerical data obtained by finite element simulation is used for building the surrogate models. These models are used for sensitivity analysis, evaluation of the weight saving parameters and for design optimization of stiffened composite panels under axial compression loading. It was shown that employing the surrogate models satisfactory accuracy can be achieved to describe the post-buckling behavior of the stiffened panels and to use these models in design optimization.

Finite element analysis of vibration and damping of laminated composites

Abstract A sandwich composite beam and plate finite superelements with viscoelastic layers for vibration and damping analysis are presented. Each layer is considered as simple Timoshenkos beam or Mindlin-Reissner plate finite element. The energy dissipation in the viscoelastic layers is taken into account with complex modulus of elasticity theory. Two methods for damping analysis of laminated composite beams or plates are considered: the method of complex eigenvalues and the energy method. The first one is an ‘exact’ method, in which the modal loss factors of structure for each frequency are determined as the ratio of imaginary and real parts of complex eigenvalues. The second method is approximate, in which the modal loss factors of structure for each frequency are calculated as the ratio of dissipated and elastic strain energy for one cycle of steady-state vibrations. For sandwich beams and plates with a viscoelastic middle layer, the vibration and damping analysis for a wide range of materials and geometric parameters was carried out. Comparison of the results obtained by the two methods gives good agreement with the results of other authors.

Vibration and damping analysis of laminated composite plates by the finite element method

The present investigation is concerned with the utilisation of the finite element technique for predicting the natural frequencies and the modal damping factor (also called the loss factor) of anisotropic fibre‐reinforced composite laminated plates. The simple definition of the modal damping factor is defined as the ratio of the strain energy dissipated per radian of vibration, in the mode of interest, to the total strain energy of the entire laminate at maximum displacement during the same cycle. Results for the vibration and damping analysis of multi‐layered plates obtained by the present methods are compared with the results obtained by other authors and with the results of experiments.

Response surface method for solution of structural identification problems

The article is focused on the application of the Response surface method for the solution of structural identification problems. The approximating functions are obtained from the data of numerical experiments, which is performed in the sample points of experimental design. A Minimal mean squared distance Latin hypercube design is used in the present article. A local approximation method is employed for building the response surfaces. An example of the application of the response surface method and experimental design for the identification of elastic properties of a laminated composite material is discussed. The five elastic constants of carbon/epoxy laminate are determined employing experimentally measured eigenfrequencies of composite plates. The identification functional represents discrepancy between experimentally measured and numerically calculated frequencies, which are dependent on the variables to be identified. The identified elastic constants have been compared with the values obtained from an independent static test. A good agreement of the results is observed.

Free Damped Vibrations of Sandwich Shells of Revolution

Using a zig-zag model the free damped vibrations of sandwich shells of revolution are investigated. As special cases the vibration analysis under consideration of damping of cylindrical, conical and spherical sandwich shells is performed. A specific sandwich shell finite element with 54 degrees of freedom is employed. Starting from the energy method the damping model is developed. Numerical examples for the free vibration analysis with damping based on the proposed finite element approach are discussed. Results for sandwich shells show a satisfactory agreement with various reference solutions.

Identification of elastic properties of composites by method of planning of experiments

Abstract A numerical-experimental method for identification of the elastic properties of laminated polymeric composites from the experimental results for eigenfrequencies of the plates is developed. The elastic properties of single layer of the laminated plate are the parameters to be identified. The approach is based on the finite element simulation of the vibration problem. By using the method of planning of experiments and the data obtained by the finite element solution simple models containing the parameters to be identified have been obtained. These simple models and the data of the vibration experiment are used to identify the elastic properties of the layer. Good agreement between the reference solutions and the results obtained by the method of planning of experiments have been observed. The proposed approach can be used as a non-destructive method in order to determine the elastic properties of the layer in the laminated composites.

Identification of Elastic Properties of Composite Laminates

This article is focused on application of the response surface method (RSM) for solution of structural identification problems. The approximating functions are obtained from the data of deterministic numerical experiment. The numerical experiment is performed in the sample points of experiment design. A minimal mean squared distance Latin hypercube (MMSDLH) design is used in the present paper. For building the response surfaces, a local approximation method is employed. An example of application of the response surface method and experiment design for identification of elastic properties of laminated composite material is discussed. Elastic properties of carbon/epoxy laminate are determined employing the experimentally measured eigenfrequencies of composite plates. The identification functional represents differences between experimentally measured and numerically calculated frequencies, which are dependent on variables to be identified. The identification parameters are five elastic constants of material. The elastic constants identified from vibration test have been compared with the values obtained from independent static test. Good agreement of the results is observed.