In mathematics, graph theory is the study of graphs, which are mathematical structures used to model pairwise relations between objects. A graph in this context is made up of vertices which are connected by edges. A distinction is made between undirected graphs, where edges link two vertices symmetrically, and directed graphs, where edges link two vertices asymmetrically; see Graph for more detailed definitions and for other variations in the types of graph that are commonly considered. Graphs are one of the prime objects of study in discrete mathematics.
Strength of materials, also called mechanics of materials, is a subject which deals with the behavior of solid objects subject to stresses and strains. The complete theory began with the consideration of the behavior of one and two dimensional members of structures, whose states of stress can be approximated as two dimensional, and was then generalized to three dimensions to develop a more complete theory of the elastic and plastic behavior of materials. An important founding pioneer in mechanics of materials was Stephen Timoshenko.
Graph drawing is an area of mathematics and computer science combining methods from geometric graph theory and information visualization to derive two-dimensional depictions of graphs arising from applications such as social network analysis, cartography, linguistics, and bioinformatics.
Stress–strain analysis is an engineering discipline that uses many methods to determine the stresses and strains in materials and structures subjected to forces. In continuum mechanics, stress is a physical quantity that expresses the internal forces that neighboring particles of a continuous material exert on each other, while strain is the measure of the deformation of the material.
A beam is a structural element that primarily resists loads applied laterally to the beam's axis. Its mode of deflection is primarily by bending. The loads applied to the beam result in reaction forces at the beam's support points. The total effect of all the forces acting on the beam is to produce shear forces and bending moments within the beam, that in turn induce internal stresses, strains and deflections of the beam. Beams are characterized by their manner of support, profile, length, and their material.
In structural geology, geological fold occurs when one or a stack of originally flat and planar surfaces, such as sedimentary strata, are bent or curved as a result of permanent deformation. Synsedimentary folds are those due to slumping of sedimentary material before it is lithified. Folds in rocks vary in size from microscopic crinkles to mountain-sized folds. They occur singly as isolated folds and in extensive fold trains of different sizes, on a variety of scales.
In science, buckling is an instability that leads to structural failure. The failure modes can in simple cases be found by simple mathematical solutions. For complex structures the failure modes are found by numerical tools.
Christian Otto Mohr was a German civil engineer.
Hardy Cross was an American structural engineer and the developer of the moment distribution method for structural analysis of statically indeterminate structures. The method was in general use from c. 1935 until c. 1960 when it was gradually superseded by other methods.
Castigliano's method, named for Carlo Alberto Castigliano, is a method for determining the displacements of a linear-elastic system based on the partial derivatives of the energy. He is known for his two theorems. The basic concept may be easy to understand by recalling that a change in energy is equal to the causing force times the resulting displacement. Therefore, the causing force is equal to the change in energy divided by the resulting displacement. Alternatively, the resulting displacement is equal to the change in energy divided by the causing force. Partial derivatives are needed to relate causing forces and resulting displacements to the change in energy.
The finite element method (FEM) is a powerful technique originally developed for numerical solution of complex problems in structural mechanics, and it remains the method of choice for complex systems. In the FEM, the structural system is modeled by a set of appropriate finite elements interconnected at discrete points called nodes. Elements may have physical properties such as thickness, coefficient of thermal expansion, density, Young's modulus, shear modulus and Poisson's ratio.
Energy principles in structural mechanics express the relationships between stresses, strains or deformations, displacements, material properties, and external effects in the form of energy or work done by internal and external forces. Since energy is a scalar quantity, these relationships provide convenient and alternative means for formulating the governing equations of deformable bodies in solid mechanics. They can also be used for obtaining approximate solutions of fairly complex systems, bypassing the difficult task of solving the set of governing partial differential equations.
Micromechanics is the analysis of composite or heterogeneous materials on the level of the individual constituents that constitute these materials.
Fluid–structure interaction (FSI) is the interaction of some movable or deformable structure with an internal or surrounding fluid flow. Fluid–structure interactions can be stable or oscillatory. In oscillatory interactions, the strain induced in the solid structure causes it to move such that the source of strain is reduced, and the structure returns to its former state only for the process to repeat.
In geometry, a vertex is a point where two or more curves, lines, or edges meet. As a consequence of this definition, the point where two lines meet to form an angle and the corners of polygons and polyhedra are vertices.
Extreme Loading for Structures (ELS) is commercial structural-analysis software based on the applied element method (AEM) for the automatic tracking and propagation of cracks, separation of elements, element collision, and collapse of structures under extreme loads. AEM combines features of Finite element method and Discrete element method simulation with its own solver capabilities for the generation of PC-based structural analysis.
Layered graph drawing or hierarchical graph drawing is a type of graph drawing in which the vertices of a directed graph are drawn in horizontal rows or layers with the edges generally directed downwards. It is also known as Sugiyama-style graph drawing after Kozo Sugiyama, who first developed this drawing style.
Sesam is a software suite for structural and hydrodynamic analysis of ships and offshore structures. It is based on the displacement formulation of the Finite Element Method.
DIANA is a Finite Element Analysis (FEA) solver developed and distributed by DIANA FEA BV and several other resellers worldwide. The software is utilised at both ends of the market, by small consultancies and global engineering consultants, research institutions and is utilised by many highly respected educational institutions worldwide in both civil and geotechnical engineering courses. DIANA is equipped with very powerful solvers which enables the analysis of a wide range of structures, large and small - with basic or advanced analyses. A large selection of material models, element libraries and analysis procedures are available within the package which gives DIANA a large degree of flexibility. The main fields of use of DIANA include design and analysis of dams & dikes; tunnels & underground structures; oil & gas & historical constructions and large reinforced concrete structures. Some of the specialised analyses available in DIANA for these fields of use include seismic analysis; fire analysis and young hardening concrete.
