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The matrix method is a structural analysis method used as a fundamental principle in many applications in civil engineering.
The method is carried out, using either a stiffness matrix or a flexibility matrix.
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The matrix method is a structural analysis method used as a fundamental principle in many applications in civil engineering.
The method is carried out, using either a stiffness matrix or a flexibility matrix.
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A composite material is a material which is produced from two or more constituent materials. These constituent materials have notably dissimilar chemical or physical properties and are merged to create a material with properties unlike the individual elements. Within the finished structure, the individual elements remain separate and distinct, distinguishing composites from mixtures and solid solutions.
In biology, the extracellular matrix (ECM) is a three-dimensional network consisting of extracellular macromolecules and minerals, such as collagen, enzymes, glycoproteins and hydroxyapatite that provide structural and biochemical support to surrounding cells. Because multicellularity evolved independently in different multicellular lineages, the composition of ECM varies between multicellular structures; however, cell adhesion, cell-to-cell communication and differentiation are common functions of the ECM.
Structural analysis is the determination of the effects of loads on physical structures and their components. Structures subject to this type of analysis include all that must withstand loads, such as buildings, bridges, aircraft and ships. Structural analysis employs the fields of applied mechanics, materials science and applied mathematics to compute a structure's deformations, internal forces, stresses, support reactions, accelerations, and stability. The results of the analysis are used to verify a structure's fitness for use, often precluding physical tests. Structural analysis is thus a key part of the engineering design of structures.
Stiffness is the extent to which an object resists deformation in response to an applied force.
In statics and structural mechanics, a structure is statically indeterminate when the static equilibrium equations - force and moment equilibrium conditions - are insufficient for determining the internal forces and reactions on that structure.
Fibre-reinforced plastic is a composite material made of a polymer matrix reinforced with fibres. The fibres are usually glass, carbon, aramid, or basalt. Rarely, other fibres such as paper, wood, or asbestos have been used. The polymer is usually an epoxy, vinyl ester, or polyester thermosetting plastic, though phenol formaldehyde resins are still in use.
Geosynthetics are synthetic products used to stabilize terrain. They are generally polymeric products used to solve civil engineering problems. This includes eight main product categories: geotextiles, geogrids, geonets, geomembranes, geosynthetic clay liners, geofoam, geocells and geocomposites. The polymeric nature of the products makes them suitable for use in the ground where high levels of durability are required. They can also be used in exposed applications. Geosynthetics are available in a wide range of forms and materials. These products have a wide range of applications and are currently used in many civil, geotechnical, transportation, geoenvironmental, hydraulic, and private development applications including roads, airfields, railroads, embankments, retaining structures, reservoirs, canals, dams, erosion control, sediment control, landfill liners, landfill covers, mining, aquaculture and agriculture.
In structural engineering, the flexibility method, also called the method of consistent deformations, is the traditional method for computing member forces and displacements in structural systems. Its modern version formulated in terms of the members' flexibility matrices also has the name the matrix force method due to its use of member forces as the primary unknowns.
As one of the methods of structural analysis, the direct stiffness method, also known as the matrix stiffness method, is particularly suited for computer-automated analysis of complex structures including the statically indeterminate type. It is a matrix method that makes use of the members' stiffness relations for computing member forces and displacements in structures. The direct stiffness method is the most common implementation of the finite element method (FEM). In applying the method, the system must be modeled as a set of simpler, idealized elements interconnected at the nodes. The material stiffness properties of these elements are then, through matrix mathematics, compiled into a single matrix equation which governs the behaviour of the entire idealized structure. The structure’s unknown displacements and forces can then be determined by solving this equation. The direct stiffness method forms the basis for most commercial and free source finite element software.
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.
A quiver tip is a flexible extension to a fishing rod which is designed to move, or quiver, when a fish takes the bait. The main characteristic of its design is its sensitivity. It is a popular and very effective method of bite indication both on still and running water. It is not used in game fishing and is seldom, if ever, used when fishing for very large coarse fish. In essence, the angler watches the tip of the fishing rod to detect bites as opposed to, say, a float or an electronic bite alarm.
Local regression or local polynomial regression, also known as moving regression, is a generalization of moving average and polynomial regression. Its most common methods, initially developed for scatterplot smoothing, are LOESS and LOWESS, both pronounced. They are two strongly related non-parametric regression methods that combine multiple regression models in a k-nearest-neighbor-based meta-model. Outside econometrics, LOESS is known and commonly referred to as Savitzky–Golay filter.
In statistics and image processing, to smooth a data set is to create an approximating function that attempts to capture important patterns in the data, while leaving out noise or other fine-scale structures/rapid phenomena. In smoothing, the data points of a signal are modified so individual points higher than the adjacent points are reduced, and points that are lower than the adjacent points are increased leading to a smoother signal. Smoothing may be used in two important ways that can aid in data analysis (1) by being able to extract more information from the data as long as the assumption of smoothing is reasonable and (2) by being able to provide analyses that are both flexible and robust. Many different algorithms are used in smoothing.
Structural mechanics or Mechanics of structures is the computation of deformations, deflections, and internal forces or stresses within structures, either for design or for performance evaluation of existing structures. It is one subset of structural analysis. Structural mechanics analysis needs input data such as structural loads, the structure's geometric representation and support conditions, and the materials' properties. Output quantities may include support reactions, stresses and displacements. Advanced structural mechanics may include the effects of stability and non-linear behaviors.
Rotordynamics, also known as rotor dynamics, is a specialized branch of applied mechanics concerned with the behavior and diagnosis of rotating structures. It is commonly used to analyze the behavior of structures ranging from jet engines and steam turbines to auto engines and computer disk storage. At its most basic level, rotor dynamics is concerned with one or more mechanical structures (rotors) supported by bearings and influenced by internal phenomena that rotate around a single axis. The supporting structure is called a stator. As the speed of rotation increases the amplitude of vibration often passes through a maximum that is called a critical speed. This amplitude is commonly excited by unbalance of the rotating structure; everyday examples include engine balance and tire balance. If the amplitude of vibration at these critical speeds is excessive, then catastrophic failure occurs. In addition to this, turbo machinery often develop instabilities which are related to the internal makeup of turbo machinery, and which must be corrected. This is the chief concern of engineers who design large rotors.
A blowing agent is a substance which is capable of producing a cellular structure via a foaming process in a variety of materials that undergo hardening or phase transition, such as polymers, plastics, and metals. They are typically applied when the blown material is in a liquid stage. The cellular structure in a matrix reduces density, increasing thermal and acoustic insulation, while increasing relative stiffness of the original polymer.
Plastic pipe is a tubular section, or hollow cylinder, made of plastic. It is usually, but not necessarily, of circular cross-section, used mainly to convey substances which can flow—liquids and gases (fluids), slurries, powders and masses of small solids. It can also be used for structural applications; hollow pipes are far stiffer per unit weight than solid members.
In the finite element method for the numerical solution of elliptic partial differential equations, the stiffness matrix represents the system of linear equations that must be solved in order to ascertain an approximate solution to the differential equation.
Carbon-fiber-reinforced polymers, carbon-fibre-reinforced polymers, or carbon-fiber-reinforced plastics, or carbon-fiber reinforced-thermoplastic, are extremely strong and light fiber-reinforced plastics that contain carbon fibers. CFRPs can be expensive to produce, but are commonly used wherever high strength-to-weight ratio and stiffness (rigidity) are required, such as aerospace, superstructures of ships, automotive, civil engineering, sports equipment, and an increasing number of consumer and technical applications.
The applied element method (AEM) is a numerical analysis used in predicting the continuum and discrete behavior of structures. The modeling method in AEM adopts the concept of discrete cracking allowing it to automatically track structural collapse behavior passing through all stages of loading: elastic, crack initiation and propagation in tension-weak materials, reinforcement yield, element separation, element contact and collision, as well as collision with the ground and adjacent structures.