Structural analysisStructural analysis is a branch of solid mechanics which uses simplified models for solids like bars, beams and shells for engineering decision making. Its main objective is to determine the effect of loads on the physical structures and their components. In contrast to theory of elasticity, the models used in structure analysis are often differential equations in one spatial variable. Structures subject to this type of analysis include all that must withstand loads, such as buildings, bridges, aircraft and ships.
Failure analysisFailure analysis is the process of collecting and analyzing data to determine the cause of a failure, often with the goal of determining corrective actions or liability. According to Bloch and Geitner, ”machinery failures reveal a reaction chain of cause and effect... usually a deficiency commonly referred to as the symptom...”. Failure analysis can save money, lives, and resources if done correctly and acted upon.
Stable distributionIn probability theory, a distribution is said to be stable if a linear combination of two independent random variables with this distribution has the same distribution, up to location and scale parameters. A random variable is said to be stable if its distribution is stable. The stable distribution family is also sometimes referred to as the Lévy alpha-stable distribution, after Paul Lévy, the first mathematician to have studied it. Of the four parameters defining the family, most attention has been focused on the stability parameter, (see panel).
Probability distributionIn probability theory and statistics, a probability distribution is the mathematical function that gives the probabilities of occurrence of different possible outcomes for an experiment. It is a mathematical description of a random phenomenon in terms of its sample space and the probabilities of events (subsets of the sample space). For instance, if X is used to denote the outcome of a coin toss ("the experiment"), then the probability distribution of X would take the value 0.5 (1 in 2 or 1/2) for X = heads, and 0.
Cauchy distributionThe Cauchy distribution, named after Augustin Cauchy, is a continuous probability distribution. It is also known, especially among physicists, as the Lorentz distribution (after Hendrik Lorentz), Cauchy–Lorentz distribution, Lorentz(ian) function, or Breit–Wigner distribution. The Cauchy distribution is the distribution of the x-intercept of a ray issuing from with a uniformly distributed angle. It is also the distribution of the ratio of two independent normally distributed random variables with mean zero.
Fatigue (material)In materials science, fatigue is the initiation and propagation of cracks in a material due to cyclic loading. Once a fatigue crack has initiated, it grows a small amount with each loading cycle, typically producing striations on some parts of the fracture surface. The crack will continue to grow until it reaches a critical size, which occurs when the stress intensity factor of the crack exceeds the fracture toughness of the material, producing rapid propagation and typically complete fracture of the structure.
Measurement uncertaintyIn metrology, measurement uncertainty is the expression of the statistical dispersion of the values attributed to a measured quantity. All measurements are subject to uncertainty and a measurement result is complete only when it is accompanied by a statement of the associated uncertainty, such as the standard deviation. By international agreement, this uncertainty has a probabilistic basis and reflects incomplete knowledge of the quantity value. It is a non-negative parameter.
Maximum entropy probability distributionIn statistics and information theory, a maximum entropy probability distribution has entropy that is at least as great as that of all other members of a specified class of probability distributions. According to the principle of maximum entropy, if nothing is known about a distribution except that it belongs to a certain class (usually defined in terms of specified properties or measures), then the distribution with the largest entropy should be chosen as the least-informative default.
Laplace distributionIn probability theory and statistics, the Laplace distribution is a continuous probability distribution named after Pierre-Simon Laplace. It is also sometimes called the double exponential distribution, because it can be thought of as two exponential distributions (with an additional location parameter) spliced together along the abscissa, although the term is also sometimes used to refer to the Gumbel distribution.
Compressive strengthIn mechanics, compressive strength (or compression strength) is the capacity of a material or structure to withstand loads tending to reduce size (as opposed to tensile strength which withstands loads tending to elongate). In other words, compressive strength resists compression (being pushed together), whereas tensile strength resists tension (being pulled apart). In the study of strength of materials, tensile strength, compressive strength, and shear strength can be analyzed independently.
