Non-linear elastic analysis of delamination in two-dimensional functionally graded multilayered beams

2019 ◽  
Vol 11 (4) ◽  
pp. 319-335 ◽  
Author(s):  
V. Rizov
Keyword(s):  
Functionally Graded ◽  
Elastic Analysis ◽  
Two Dimensional ◽  
Linear Elastic ◽  
Non Linear

Implementation of p and h-p Versions of the Finite Element Method

1992 ◽  
Author(s):  
Ye-Chen Lai ◽  
Timothy C. S. Liang ◽  
Zhenxue Jia
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Elastic Analysis ◽  
Two Dimensional ◽  
The Finite Element Method ◽  
Shape Functions ◽  
Linear Elastic ◽  
Finite Element Software ◽  
Analysis Process ◽  
Adaptive Analysis

Abstract Based on hierarchic shape functions and an effective convergence procedure, the p-version and h-p adaptive analysis capabilities were incorporated into a finite element software system, called COSMOS/M. The range of the polynomial orders can be varied from 1 to 10 for two dimensional linear elastic analysis. In the h-p adaptive analysis process, a refined mesh are first achieved via adaptive h-refinement. The p-refinement is then added on to the h-version designed mesh by uniformly increasing the degree of the polynomials. Some numerical results computed by COSMOS/M are presented to illustrate the performance of these p and h-p analysis capabilities.

Three-dimensional deformations in a single-lap joint

1994 ◽  
Vol 29 (2) ◽  
pp. 137-145 ◽  
Author(s):  
M Y Tsai ◽  
J Morton
Keyword(s):  
Three Dimensional ◽  
Two Dimensional ◽  
Stress Distributions ◽  
Lap Joint ◽  
Displacement Fields ◽  
Element Analysis ◽  
Linear Elastic ◽  
Non Linear ◽  
Linear Effects ◽  
Peel Stress

The three-dimensional nature of the state of deformation in a single-lap test specimen is investigated in a linear elastic finite element analysis in which the boundary conditions account for the geometrically non-linear effects. The validity of the model is demonstrated by comparing the resulting displacement fields with those obtained from a moiré inteferometry experiment. The three-dimensional adherend and adhesive stress distributions are calculated and compared with those from a two-dimensional non-linear numerical analysis, Goland and Reissner's solution, and experimental measurements. The nature of the three-dimensional mechanics is described and discussed in detail. It is shown that three-dimensional regions exists in the specimen, where the adherend and adhesive stress distributions in the overlap near (and especially on) the free surface are quite different from those occurring in the interior. It is also shown that the adhesive peel stress is extremely sensitive to this three-dimensional effect, but the adhesive shear is not. It is also observed that the maximum value of the peel stress occurs at the end of the overlap in the central two-dimensional core region, rather than at the corners where the three-dimensional effects are found. The extent of three-dimensional regions is also quantified.

Non-linear delamination in two-dimensional functionally graded multilayered beam

2018 ◽  
Vol 9 (5) ◽  
pp. 646-663
Author(s):  
Victor Rizov
Keyword(s):  
Mechanical Behaviour ◽  
Fracture Behaviour ◽  
Strain Energy Release ◽  
Functionally Graded ◽  
Integral Approach ◽  
Two Dimensional ◽  
Content Type ◽  
Crack Location ◽  
Delamination Fracture ◽  
Non Linear

Purpose A delamination fracture analysis of two-dimensional functionally graded multilayered end-loaded split beam configuration with non-linear mechanical behaviour of material is conducted. The beam is made of an arbitrary number of longitudinal layers. Perfect adhesion between layers is assumed. The material is two-dimensional functionally graded in the cross-section of each layer. Also, each layer has individual thickness and material properties. A delamination crack is located arbitrary along the beam height. The paper aims to discuss these issues. Design/methodology/approach The delamination fracture behaviour is investigated analytically in terms of the strain energy release rate by analysing the balance of the energy. An additional analysis of the delamination fracture is performed by applying the J-integral approach for verification. Findings The solutions derived are used to evaluate the effects of crack location, material gradients and material non-linearity on the delamination fracture behaviour of end-loaded split beam. The effect of material gradient on the distribution of the J-integral value along the crack front is elucidated too. Originality/value Delamination in the multilayered functionally graded end-loaded split beam exhibiting non-linear mechanical behaviour of the material is analysed assuming that the material property is distributed non-linearly in both thickness and width directions in each layer.

Non-linear fracture in bi-directional graded shafts in torsion

2019 ◽  
Vol 15 (1) ◽  
pp. 156-169 ◽  
Author(s):  
Victor Rizov
Keyword(s):  
Release Rate ◽  
Strain Energy ◽  
Strain Energy Release Rate ◽  
Fracture Behaviour ◽  
Strain Energy Release ◽  
Functionally Graded ◽  
Content Type ◽  
Linear Elastic ◽  
Stress Strain Relation ◽  
Non Linear

Purpose The purpose of this paper is to develop an analysis of longitudinal fracture behaviour of a functionally graded non-linear-elastic circular shaft loaded in torsion. It is assumed that the material is functionally graded in both radial and longitudinal directions of the shaft (i.e. the material is bi-directional functionally graded). Design/methodology/approach The Ramberg–Osgood stress-strain relation is used to describe the non-linear mechanical behaviour of the functionally graded material. The fracture is studied in terms of the strain energy release rate by analysing the balance of the energy. The strain energy release rate is obtained also by differentiating of the complementary strain energy with respect to the crack area for verification. Findings Parametric studies are carried out in order to evaluate the influence of material gradients in radial and longitudinal directions, the crack location in radial direction and the crack length on the fracture behaviour of the shaft. It is found that by using appropriate gradients in radial and longitudinal directions, one can tailor the variations of material properties in order to improve the fracture performance of the non-linear-elastic circular shafts to the externally applied torsion moments. Originality/value A longitudinal cylindrical crack in a bi-directional functionally graded non-linear-elastic circular shaft loaded in torsion is analysed by using the Ramberg–Osgood stress-strain relation.

A method for the derivation of load effect envelopes based on statistical considerations

1993 ◽  
Vol 20 (2) ◽  
pp. 201-209
Author(s):  
Eugene J. O'Brien ◽  
Robert E. Loov
Keyword(s):  
Structural Analysis ◽  
Three Dimensional ◽  
Elastic Analysis ◽  
Two Dimensional ◽  
Statistical Parameters ◽  
Simple Method ◽  
Load Effect ◽  
Linear Elastic ◽  
Derived Design ◽  
Usual Process

A simple method is proposed as a substitute for the usual process of factoring loads, performing a linear elastic analysis, and determining an envelope of the results. The method is based on statistical principles, but only a minimum knowledge of statistics is required for its use. It involves conventional structural analysis followed by some processing of the results which could readily be incorporated into existing computer programs.The practice of performing two-dimensional analyses on parts of three-dimensional structures is possible with the proposed approach. The implications are clarified and the necessary statistical parameters are derived.Deterministically derived design envelopes represent all the extremes of loading that can reasonably be considered. The envelopes found by the new method not only reflect loading variations but also consider their relative probabilities of occurrence so that excursions beyond the envelope are expected to be equally infrequent along the entire length of the structure. Inconsistencies inherent in the conventional approach are highlighted by comparison with the proposed method for a number of examples. Key words: probabilistic, safety, load, imposed load, load effect envelope, building.

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