Donald W. Kelly

Interpreting load paths and stress trajectories in elasticity

Design engineers use the term load path to describe, in general terms, the way in which loads path through a structure from the points of application to the points where they are reacted. In contrast, stress trajectories are more clearly identified by the direction of the principal stress vectors at a point. The first author proposed a simple definition of the term load path in 1995 and proposed procedures to determine load paths from two‐dimensional finite element solutions. In this paper, the concept of load paths will be further explored and related to stress trajectories and Michell structures. The insight given when determining the load transfer near a pin‐loaded hole will be demonstrated. In addition a cantilevered beam will be considered and an introduction to plotting load paths in three‐dimensional structures is given.

Experimental Investigation of Dynamically Loaded Bolted Joints in Carbon Fibre Composite Structures

This paper presents quasi-static and dynamic modelling of bolted composite structures using the explicit finite element code PAM-CRASH. User controlled point link (PLINK) elements were investigated for modelling the bolted composite joints used in the structures. Simulation results were compared with quasi-static and dynamic structural testing reported previously. Two loading configurations were considered. It was shown that the PLINK element modelling approach agreed well with the experimental results for both loading configurations and for one case offered significant improvements over other simplified bolt modelling methods. A stacked shell modelling approach was used to model the interlaminar delamination damage present in the ball-loaded impact mode. The overall response of the structure was significantly improved by the addition of these energy absorbing interfaces.

Knowledge-based engineering system to estimate manufacturing cost for composite structures

Acosting application utilizing the knowledge-based-engineering environment inCATIAV5 has been developed in this research. The application can be used to estimate the cost of an assembly of composite components modeled in CATIA V5 during the initial conceptual design phase. The assembly cost is determined by extracting manufacturing process costings from a process cost analysis database. The tool uses design rules for aerospace structures to add detail to a conceptual design enabling an estimate of the cost to be determined. In addition, the tool can modify the structures to achieve the design goal of compliance with performance criteria with minimum weight. The tool is thus able to answer “what-if” questions as the design concept evolves.

A procedure for determining load paths in elastic continua

The determination of load paths is an essential element of structural design. Load paths provide insight into the way the structure is performing its prescribed function. They can also indicate possibilities for shape optimization and the effect of component modification or damage. They are relatively easy to define in simple structures such as trusses which comprise a finite number of clearly defined members which carry only axial load. The load path is given simply by tracing the higher axial loads through the structure. However, for continua such as plates or solids, there is currently no systematic procedure for determining the path of load from the point of application to the constrained boundaries. This paper addresses the problem of defining the path of loads in plates with geometric discontinuities and in simple joints. The theory associated with the determination of the load path is first introduced, and then integrated into a finite element package to provide pictorial contours.

Load paths and load flow in finite element analysis

A procedure for plotting load paths and load flow in structures from a finite element analysis is described. The load flow is indicated by pointing vectors and the load paths are determined by plotting contours tangent to these vectors. The procedure is applied to assembled structures. An explanation is given for “eddies” that can appear in regions not contributing to the load path.

Free and forced vibration analysis using improved third-order shear deformation theory for functionally graded plates under high temperature loading

An improved third-order shear deformation theory is employed to investigate free and forced vibration responses of functionally graded plates. A power law distribution is used to describe the variation of material compositions across the plate thickness. The governing equations for vibration analysis obtained using an energy approach are then solved using the Ritz method. Two types of solutions, temperature independent and dependent material properties, are considered. Many effects of the volume fraction index, temperature, material pairs, thickness, plate aspect ratio, etc., which have significant impact on dynamic behaviour of the plates, are considered in the numerical illustrations of free and forced vibration results. At high temperatures, it is observed that the maximum deflections of the functionally graded plates subjected to the dynamic loading increase with the increase of frequency ratio and temperature.

A Posteriori Error Estimators and Adaptivity for Finite Element Approximation of the Non-Homogeneous Dirichlet Problem

Techniques are developed for a posteriori error analysis of the non-homogeneous Dirichlet problem for the Laplacian giving computable error bounds for the error measured in the energy norm. The techniques are based on the equilibrated residual method that has proved to be reliable and accurate for the treatment of problems with homogeneous Dirichlet data. It is shown how the equilibrated residual method must be modified to include the practically important case of non-homogeneous Dirichlet data. Explicit and implicit a posteriori error estimators are derived and shown to be efficient and reliable. Numerical examples are provided illustrating the theory.

An algorithm for defining load, paths and a load bearing topology in finite element analysis

Purpose – The purpose of this paper is to describe a post‐processing procedure for defining load paths and a load bearing topology using the stresses from a finite element analysis.Design/methodology/approach – Cauchy stress vectors and a Runge‐Kutta algorithm are used to identify the paths being followed by load components aligned with the coordinate axes. An algorithm is then defined which identifies an efficient topology that will carry the loads by straightening the paths.Findings – The aim of the algorithm is to provide insight into the way a structure is carrying loads by identifying the material most effective in performing the load transfer. The procedure is applied to a number of structures to demonstrate its applicability to structural design.Research limitations/implications – The examples demonstrate an insight of structural behavior that is useful at the conceptual stage of the design process. The load paths identify load transfer and warn the designer of the creation of bending moments and t...

A posteriori error estimates in finite difference techniques

Abstract A technique is described which defines an upper bound for the effect of the truncation error on finite difference solutions to elliptic boundary value problems. This technique does not attempt to provide an estimate which can be used to correct the finite difference solution but rather to produce a guaranteed upper bound measure of the error which can be used to assess the quality of the solution. Application to two problems is given to demonstrate the basic features of the analysis which is implemented in a post-processing mode once the original solution has been completed.

Molecular dynamics study on effects of aspect ratio of carbon nanotubes in thermosetting epoxy based nanocomposites including modeling of crosslinking process

Abstract A comprehensive modeling and simulation approach using molecular dynamics (MD) is presented in this paper. The influence of aspect ratio of carbon nanotubes (CNTs) in thermosetting epoxy is studied using MD. The thermo-mechanical properties of epoxy models reinforced by CNTs with various aspect ratios are extracted. CNTs with the higher aspect ratio increase stiffness of the epoxy resin with facilitating premature yield in tension while a noticeable degradation in thermal properties is evidenced. The evolution of internal energy during straining shows that CNTs prolong the constant transition rate of dihedral and van der Waals energy in the elastic region. This might delay conformational changes of epoxy molecules to the lower energy level. Free volume and pair distribution function studies of the molecular models with CNTs compared with the neat epoxy model provide the plausible conclusion that the steric hindrance of CNTs in the three-dimensional epoxy molecular domain may result in the less dense structure of the epoxy.