L. Ragulskis

Plotting isoclinics for hybrid photoelasticity and finite element analysis

Displacement-based finite element method formulations are coupled with stress-based photoelasticity analysis. As the stress field is discontinuous at the interelement boundaries, the introduced smoothing procedure enables the generation of high-quality digital images acceptable for hybird experimental-numerical techniques. The proposed methods are applicable for the analysis of static and dynamic results of experimental photoelasticity.

Order adaptive integration rule with equivalently weighted internal nodes

Purpose – To develop order adaptive integration rule without limitation requiring that the number of equally spaced nodes must be a divisible numeral. Such integration technique could be of great practical value for different engineering applications where partition adaptability is impossible and use of standard high order integration techniques is unfeasible due to the fact that a significant number of nodes at the end of the sampling sequence must be deleted until the needed divisibility of the number of nodes is achieved.Design/methodology/approach – Finite element approximation is used for the subdivision of the domain of integration and the development of order adaptive integration rule.Findings – New integration rule is developed. It has a number of interesting features. Weights of the internal nodes are equivalent and equal to one. That makes the computational implementation of the integration rule very easy. Weights not equal to one are located only at the beginning and at the end of the sequence ...

Applicability of time-average fluid holography for analysis of propagating waves

Numerical procedures for construction of digital patterns of fringes mimicking fluid holograms are developed. Because conventional finite-element fluid analysis techniques are based on the approximation of nodal displacements, conjugate smoothing of the values of volumetric strain is performed in order to obtain realistic holographic images. Two-dimensional fluid oscillations are analyzed using the developed techniques. It is shown that though time-average fluid holography is a powerful optical experimental method for analysis of short-term transient processes and harmonic vibrations, it has rather limited applicability to studying propagating waves.

Generalized Abel transform for the analysis of fluid vibration in a tube

Fluid vibrations in axisymmetric geometry according to the first harmonic in the circumferential direction are analyzed. This problem has a practical application in the analysis of transverse vibrations of fluid in an axisymmetric pipe. The numerical model is developed using finite-element techniques in axisymmetric geometry. Irrotational motions of ideal compressible fluid are analyzed. The finite-element model of the system is based on the approximation of nodal displacements via the shape functions. Thus the field of the amplitudes of the circumferential variation of the volumetric strain is calculated, exploiting conjugate approximation techniques. Obtained volumetric strains are used for the numerical construction of the interference pattern of the vibrating fluid. For this purpose the Abel transform, which is usually exploited in axisymmetric problems, is generalized for problems with circumferential variation of displacements. The obtained interference patterns are used in hybrid experimental–numerical procedures and help to interpret experimental results.

Shock process dynamics analysis in macro- and microscale contact systems

The dynamics of a contact type system is analyzed in the regimes of singular and periodic shock processes. Governing equations of motion and their analysis is presented for one-dimensional system model. Examples of the design of different contacting elements is presented together with the numerical modeling results. The construction of the contacting elements, particularly the cantilever plate is optimized using numerical and laser holographical analysis.

Generalised Abel transform for the analysis of fluid vibrations

Development of hybrid numerical-experimental techniques is an important method of analysis used for interpretation and validation of experimental results. Laser holography is a powerful experimental technique for analysis of high frequency vibrations of the fluid, especially when the amplitudes of those vibrations are relatively small. It is assumed that the angular frequency of excitation coincides with the eigenfrequency of the appropriate eigenmode and thus the eigenproblem is solved. The problem of fluid eigen-vibrations in axi-symmetric geometry according to the first harmonic in the circumferential direction is analyzed. This problem has a practical application in the analysis of transverse vibrations of the fluid in an axi-symmetric pipe. The numerical model is developed on the basis of the finite element model of the fluid and the method of analysis of the problems with axi-symmetric geometry. The irrotational motions of the ideal compressible fluid are analyzed. The numerical model of the system is based on the approximation of nodal displacements via the shape functions. Thus the field of the amplitudes of the circumferential variation of the volumetric strain is calculated using the procedure of conjugate approximation. By using the procedure of conjugate approximation the amplitudes of circumferential variation of nodal volumetric strains for the eigenmodes are determined. The obtained field of volumetric strain is used in the numerical procedure for the construction of the digital holographic image. Thus the calculation of the amplitudes of circumferential variation of nodal volumetric strains consists of two stages: 1) calculations using the displacement formulation for the first harmonic in the circumferential direction by the method of finite elements; 2) determination of the field of the amplitudes of the circumferential variation of the volumetric strain by using the procedure of conjugate approximation. The obtained nodal values of the amplitudes of the circumferential variation of the volumetric strain are used in the construction of the digital holographic images. For this purpose the Abel transform which is usually used in axi-symmetric problems is generalized for the problems with axi-symmetric geometry with the variation of displacements according to the first harmonic in the circumferential direction. On the basis of the generalized Abel transform the digital holographic images are constructed. The obtained digital holographic images are used in the hybrid experimental-numerical procedure for the determination of the correlation with the experimental holographic images.

Shearographic technique for NDE analysis of high frequency bending vibrations of microstructures

Investigation of dynamics of micro electromechanical systems (MEMS) is an important problem of engineering, technology and metrology. Specifically, recent interest in applying MEMS technology to miniaturization of relays, sensors, actuators for variety of applications requires design of appropriate testing and measurement tools for investigation of dynamic properties of those systems. Therefore, application of measurement technologies capable of detecting the dynamic properties of micro scale systems may help to understand and evaluate the functionality of those systems. The shearographic technique for the detection of the transverse displacements of micro-cantilevers with respect to the shearing direction is presented. The method is expanded upto a hybrid numerical-experimental approach and includes the generation of shearographic images of the microstructures using finite element methods. The presented analysis is based on modeling NDE shearographic method and microstructures behavior.

Hybrid numerical-experimental holographic fluid interferometry

Fluid holography enables effective analysis of high speed flow problems, high frequency vibrations of micro-scale components and fluids in dosing and contacting units, high speed processes taking place in biological and chemical microsystems. The investigation of the high frequency vibrations of the fluid is an important problem in the design of various devices. Though the production stage of the interferograms is technically not extremely complicated, the interpretation of the produced fringes faces a number of mathematical and numerical problems. That is related with the complex geometry of the phase-shifting media. Under such circumstances the density can change along the line of sight, and the density is no longer proportional to phase. Therefore, development of hybrid numerical-experimental fluid holographic methods is important both for the interpretation of experimental results and for the analysis of systems in the virtual environments by generating realistic interferograms. In this paper the method of holographic interferometry is used for the analysis of the two-dimensional fluid problem. FEM analysis techniques are based on the approximation of nodal displacements (not the volumetric strains) via the shape functions. Conventional FEM would require unacceptably dense meshing for producing sufficiently smooth images. Therefore the technique for smoothing of the generated images representing the distribution of the volumetric strains and calculated from the displacement distribution is developed. The smoothing technique is based on conjugate approximation used for the calculation of nodal values of stresses and enables to obtain the images of better quality on a coarse mesh by using the displacement formulation for the calculation of the eigenmodes.