Optimum Material Disposition in 2D In-plane Bending Problems – Nodes in Motion Strategy

Abstract

Structural Optimization is the process of making high performance structures by identification and removal of un-necessary elements and material without affecting its functional , safety, serviceability and durability requirements. An optimized structure naturally leads to savings in cost and time. The present research work is n the direction of devising an optimum structure that adopts the best use of material at its best location in its best form under the given conditions. Finite Element Method has opened up ways to analyse complicated structures subjected to arbitrary loading with the required amount of accuracy demanded by an analyser. Realizing the limitations of FEM, a technique called Moving Polynomial Moving Least Square (MPMLS) has been formulated for smoothing and interpolation of stress values at any location in 2D continuum structures subjected to in-plane bending. Optimum material disposition is achieved by relocation of material to its best position by the assessment of material utilization at any given location and using the required quantity to just satisfy the conditions. A novelty called ‘Nodes in Motion’ strategy has been conceptualised to facilitate guided movement of under- utilized material to its best location in the optimum quantity. The conceptualisation, mathematical formulation, implementation and verification have been presented at every milestone of development. The results obtained have shown adoptability of the procedure for the optimum design of 2D structures subjected to in-plane bending. The potential uses of the present research findings and scope for future work have been presented.