New nine-node Lagrangian quadrilateral plate element based on Mindlin-Reissner theory using IFM

This paper presents a new nine-node Lagrangian quadrilateral plate bending element (MQP9) using the Integrated Force Method (IFM) for the analysis of thin and moderately thick plate bending problems. Three degrees of freedom: transverse displacement w and two rotations theta(x) and theta(y) are considered at each node of the element. The Mindlin-Reissner theory has been employed in the formulation which accounts the effect of shear deformation. Many standard plate bending benchmark problems have been analyzed using the new element MQP9 for various grid sizes via Integrated Force Method to estimate defections and bending moments. These results of the new element MQP9 are compared with those of similar displacement-based plate bending elements available in the literature. The results are also compared with exact solutions. It is observed that the presented new element MQP9 is free from shear locking and produced, in general, excellent results in all plate bending benchmark problems considered.

Tailoring the second mode of Euler-Bernoulli beams: an analytical approach

In this paper, we study the inverse mode shape problem for an Euler-Bernoulli beam, using an analytical approach. The mass and stiffness variations are determined for a beam, having various boundary conditions, which has a prescribed polynomial second mode shape with an internal node. It is found that physically feasible rectangular cross-section beams which satisfy the inverse problem exist for a variety of boundary conditions. The effect of the location of the internal node on the mass and stiffness variations and on the deflection of the beam is studied. The derived functions are used to verify the p-version finite element code, for the cantilever boundary condition. The paper also presents the bounds on the location of the internal node, for a valid mass and stiffness variation, for any given boundary condition. The derived property variations, corresponding to a given mode shape and boundary condition, also provides a simple closed-form solution for a class of non-uniform Euler-Bernoulli beams. These closed-form solutions can also be used to check optimization algorithms proposed for modal tailoring.

Handling large variations in mechanics: Some applications

There is a need to use probability distributions with power-law decaying tails to describe the large variations exhibited by some of the physical phenomena. The Weierstrass Random Walk (WRW) shows promise for modeling such phenomena. The theory of anomalous diffusion is now well established. It has found number of applications in Physics, Chemistry and Biology. However, its applications are limited in structural mechanics in general, and structural engineering in particular. The aim of this paper is to present some mathematical preliminaries related to WRW that would help in possible applications. In the limiting case, it represents a diffusion process whose evolution is governed by a fractional partial differential equation. Three applications of superdiffusion processes in mechanics, illustrating their effectiveness in handling large variations, are presented.

Damage assessment of composite plate structures with material and measurement uncertainty

Composite materials are very useful in structural engineering particularly in weight sensitive applications. Two different test models of the same structure made from composite materials can display very different dynamic behavior due to large uncertainties associated with composite material properties. Also, composite structures can suffer from pre-existing imperfections like delaminations, voids or cracks during fabrication. In this paper, we show that modeling and material uncertainties in composite structures can cause considerable problein in damage assessment. A recently developed C-0 shear deformable locking free refined composite plate element is employed in the numerical simulations to alleviate modeling uncertainty. A qualitative estimate of the impact of modeling uncertainty on the damage detection problem is made. A robust Fuzzy Logic System (FLS) with sliding window defuzzifier is used for delamination damage detection in composite plate type structures. The FLS is designed using variations in modal frequencies due to randomness in material properties. Probabilistic analysis is performed using Monte Carlo Simulation (MCS) on a composite plate finite element model. It is demonstrated that the FLS shows excellent robustness in delamination detection at very high levels of randomness in input data. (C) 2016 Elsevier Ltd. All rights reserved.