Jüri Majak

Weak formulation based Haar wavelet method for solving differential equations

The Haar wavelet based discretization method for solving differential equations is developed. Nonlinear Burgers equation is considered as a test problem. Both, strong and weak formulations based approaches are discussed. The discretization scheme proposed is based on the weak formulation. An attempt is made to combine the advantages of the FEM and Haar wavelets. The obtained numerical results have been validated against a closed form analytical solution as well as FEM results. Good agreement with the exact solution has been observed.

Modelling and optimal design of sheet metal RP&M processes

Purpose – To study the influence of process and product parameters on the properties of products in incremental sheet metal‐forming; to create models for process optimisation and to introduce an approach to incremental forming process optimisation.Design/methodology/approach – A new flexible sheet metal‐forming technique, incremental forming, has been studied. The technique can be viewed as a rapid prototyping/manufacturing technique for sheet metal parts. To analyse the process, an experimental study and finite element analysis were performed. For the optimal design of incremental forming process non‐linear mathematical programming was used. To estimate the limitations and main parameters of the process, a complex model was developed.Findings – Introducing optimisation procedures for the incremental forming process allows users to increase productivity and to assure quality.Research limitations/implications – As finite element analysis of the process is time‐consuming in real life situations, a future st...

Haar wavelet method for vibration analysis of nanobeams

Abstract In the current study the Haar wavelet method is adopted for free vibration analysis of nanobeams. The size-dependent behavior of the nanobeams, occurring in nanostructures, is described by Eringen nonlocal elasticity model. The accuracy of the solution is explored. The obtained results are compared with ones computed by finite difference method. The numerical convergence rates determined are found to be in agreement with corresponding convergence theorems.

An algorithm for localised and diffuse necking analysis

An analysis of localised and diffuse necking in orthotropic sheet metals is performed. Numerical algorithm covering different yield criteria and strain hardening laws is developed. The numerical algorithm proposed is based on plastic instability criterion derived in tensor notation. The capabilities of the instability criteria derived are improved using different anisotropic yield criteria and strain hardening laws. The obtained results are validated against experimental test results and compared with the results available in literature. The material parameters identification procedure for advanced yield criterion BBC2003 is treated. The Computer Algebra Systems (CAS-es) method is employed for material parameters identification. Simplicity and low computational cost of numerical analysis is achieved by the use of Hill and Swift instability conditions and empirical stress-strain relation. [Received 7 March 2007; Accepted 10 July 2007]

Embedded Electronics Influence on the Strength of Carbon Fiber Laminate

A complex electronics circuit placeholder is embedded in the carbon fiber laminate. The reduction of the material mechanical strength is assessed. The strain interaction between electronics and carbon fiber laminate is measured with digital image correlation based deformation scanner GOM ARAMIS 2M. A finite element analysis model is developed and validated. Based on FEA results the response model for prediction of the mechanical properties of laminate is introduced.

Experimental modal analysis of maritime composite panel

The investigation of dynamics of the real-life natural vibrations in structures, compared with the simulated by finite-element model frequency values and their variations, could be used for monitoring of the structural health of the composite materials. Experimental modal analysis of an example maritime composite panel is presented in the current work. The previously developed setup of the measurement system of the acceleration data for the structural health monitoring has been re-used. The results are analysed and compared with theoretically simulated results. The appropriate settings of modal analysis and their initial values for modal analysis techniques have been identified experimentally, to extract (estimate) the natural frequencies with reasonable accuracy and computational complexity.

ISF process model development

Incremental Sheet Forming (ISF) process modelling is studied. Main attention is paid to safe manufacturing. Experimental, numerical and theoretical study is performed in order to determine the material formability and the forming load components. ISF strategies for determining the Forming Limit Diagram (FLD) are pointed out. The obtained experimental results have been found to be in good agreement with theoretical considerations. The effect of plastic anisotropy of metal sheets is considered in theoretical models and test design. The obtained results allow to predict tool and material failure in ISF process. [Received 5 June 2007; Accepted 5 July 2007]