Failure Criteria

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It is not clear exactly how a rock fails, either in terms of the precise details of each micro crack initiation and Propagation or in terms of the total structural breakdown as many micro cracks propagate and coalesce. In both cases, the process is extremely complex and not subject to convenient characterization through simplified models. Nevertheless, as engineers, we should like some measure of the failure properties and the ability to predict when failure will occur. The strength criteria of rock materials can be divided into three major groups: theoretical failure criteria, experimental and curve fitting based criteria. And the last set of them is composed of two mentioned sets of failure criteria. The Mohr-Coulomb criterion expresses the relation between the shear stress and the normal stress at failure. The plane Griffith criterion which locates in theoretical group, express the uniaxial tensile strength in terms of the strain energy required to propagate micro cracks. One of the most widely used empirical strength criterion for intact rock and rock masses is Hoek-Brown Criterion. In this paper we present outlines of these criteria and focus on the Hoek-Brown criterion. The method of research is based on books and articles published in authoritative publications and journals. As a result, various types of rock failure criteria are classified and some useful suggestions regarding presented criteria have been presented. Empirical criteria, Specially Hoek and Brown Criterion, Which are in good correlations with real conditions, can be significantly much more efficient in the rock mechanics problems.

Our project deals with the design optimization of 2D (planar) and 3D (space) steel frame truss by using genetic algorithm (GA) in MATLAB. A truss is an assemblage of long, slender structural elements that are connected at their ends. Trusses find substantial use in modern construction, for instance as towers, bridges, scaffolding, etc. GA is an artificial intelligence which is used to generate best problem solution for Optimization. MATLAB is a programming tool for numerical computation, visualization and optimization.
A benchmark study on sphere function for minimization is performed and validating the GA. Similarly, a program is developed in MATLAB for Finite element method (FEM) of plane and space truss, validated with Ansys 12.0.
Case studies of 10 bar plane truss and 25 bar space truss are presented. In order to consider design problem, GA has been linked with FEM. Here the optimization of the cross-sectional area of frame truss is considered in order to obtain the minimum weight for static analysis. The cross-sectional areas are the variables which should be within certain limits in order to obtain solutions.
This led to the conclusion that a particular structural shape together with its dimensions would give the optimal solution in truss design in terms of minimum weight to support the given load, which would then translate into savings in the cost of the structural member.

A computational model was developed to simulate and predict failure response of fibrous composite panels subjected to drop-weight impact on un-partitioned fibrous composite panels using finite element analysis. The mathematical formulation consisting ...