Minimisation of the Discretisation Error in Mass and Stiffness Formulations by an Inverse Method
H Ahmadian (Liverpool University), MI Friswell (University of Wales Swansea) & JE Mottershead (Liverpool University)
International Journal for Numerical Methods in Engineering, Vol. 41, No. 2, January 1998, pp. 371-387
This paper is concerned with the formulation of mass and stiffness matrices. In the direct approach one uses assumed shape functions to develop the mass and stiffness terms. Alternatively, we may construct the matrices by using an inverse approach; the terms are assigned so that the difference between an analytical model and a numerical (discrete) one is minimised. Here we show that more accurate models can be obtained by the latter approach. The accuracy of rod, beam and plate elements that have been developed by both of the approaches are discussed, and an accurate model of a rectangular plate element is obtained by using the inverse method. The superior performance of the new element compared to other established models is demonstrated for the cases of static and dynamic response of a clamped plate.
This material has been published in the International Journal for Numerical Methods in Engineering, Vol. 41, No. 2, January 1998, pp. 371-387. Unfortunately the copyright agreement with Wiley InterScience does not allow for the PDF file of the paper to be available on this website. However the paper is available from the Wiley website - see the link below.
Link to paper using doi:10.1002/(SICI)1097-0207(19980130)41:2<371::AID-NME288>3.0.CO;2-R
International Journal for Numerical Methods in Engineering on Wiley InterScience