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The applied element method (AEM) is a numerical analysis used in predicting the continuum and discrete behavior of structures. The modeling method in AEM
Applied_element_method
Numerical method for solving physical or engineering problems
Finite element method (FEM) is a popular method for numerically solving differential equations arising in engineering and mathematical modeling. Typical
Finite_element_method
Method of solving linear partial differential equations
The boundary element method (BEM) is a numerical computational method of solving linear partial differential equations (PDEs) arising in engineering and
Boundary_element_method
software based on the applied element method (AEM) for the automatic tracking and propagation of cracks, separation of elements, element collision, and collapse
Extreme Loading for Structures
Extreme_Loading_for_Structures
Formulation of the finite element method
equations, a topic in mathematics, the spectral element method (SEM) is a formulation of the finite element method (FEM) that uses high-degree piecewise polynomials
Spectral_element_method
infinite element method is a numerical method for solving problems of engineering and mathematical physics. It is a modification of finite element method. The
Infinite_element_method
Numerical method
A discrete element method (DEM), also called a distinct element method, is any of a family of numerical methods for computing the motion and effect of
Discrete_element_method
Building collapse type
the columns, and bracing members designed to carry gravity loads. Applied element method Extreme Loading for Structures Structural robustness Cascading failure
Progressive_collapse
In numerical analysis, a mixed finite element method, is a variant of the finite element method in which extra fields to be solved are introduced during
Mixed_finite_element_method
Branch of numerical analysis
Multigrid methods can be applied in combination with any of the common discretization techniques. For example, the finite element method may be recast
Numerical methods for partial differential equations
Numerical_methods_for_partial_differential_equations
Class of numerical simulation algorithms
Smoothed finite element methods (S-FEM) are a particular class of numerical simulation algorithms for the simulation of physical phenomena. It was developed
Smoothed finite element method
Smoothed_finite_element_method
The analytic element method (AEM) is a numerical method used for the solution of partial differential equations. It was initially developed by O.D.L. Strack
Analytic_element_method
Topics referred to by the same term
of the Explorer program Applied and Environmental Microbiology, a scientific research journal Applied element method, a method of structural analysis Atlantic
AEM
Methods for solving differential equations
In applied mathematics, discontinuous Galerkin methods (DG methods) form a class of numerical methods for solving differential equations. They combine
Discontinuous_Galerkin_method
Approach to finding numerical solutions of ordinary differential equations
In mathematics and computational science, the Euler method (also called the forward Euler method) is a first-order numerical procedure for solving ordinary
Euler_method
Method for solving continuous operator problems (such as differential equations)
finite element method, the boundary element method for solving integral equations, Krylov subspace methods. Let us introduce Galerkin's method with an abstract
Galerkin_method
2003 to create structural analysis software tools utilizing the Applied Element Method (AEM) . ASI provides services including structural vulnerability
The_Steel_Network,_Inc.
This is a list of notable software packages that implement the finite element method for solving partial differential equations. This table is contributed
List of finite element software packages
List_of_finite_element_software_packages
The fuzzy finite element method combines the well-established finite element method with the concept of fuzzy numbers, the latter being a special case
Fuzzy_finite_element
Interval boundary element method is classical boundary element method with the interval parameters. Boundary element method is based on the following
Interval boundary element method
Interval_boundary_element_method
Chemical element with atomic number 85 (At)
Astatine is a chemical element; it has symbol At and atomic number 85. It is the rarest naturally occurring element in the Earth's crust, occurring only
Astatine
Study of the response of buildings and structures to earthquakes
scenarios. This has led to the emergence of methods like the incremental dynamic analysis. Applied element method Earthquake simulation Extreme Loading for
Seismic_analysis
Application of mathematical methods to other fields
Applied mathematics is the application of mathematical methods by different fields such as physics, engineering, medicine, biology, finance, business,
Applied_mathematics
Technique to solve geological problems by computational simulation
mass and energy. The finite volume method can be applied on irregular meshes like the finite element method. The element equations are still physically meaningful
Numerical_modeling_(geology)
interval finite element method (interval FEM) is a finite element method that uses interval parameters. Interval FEM can be applied in situations where
Interval_finite_element
Class of numerical techniques
common approaches to the numerical solution of PDE, along with finite element methods. For a n-times differentiable function, by Taylor's theorem the Taylor
Finite_difference_method
Interval finite element Applied element method — for simulation of cracks and structural collapse Wood–Armer method — structural analysis method based on finite
List of numerical analysis topics
List_of_numerical_analysis_topics
Numerical method used in structural mechanics
The finite element method (FEM) is a powerful technique originally developed for the numerical solution of complex problems in structural mechanics, and
Finite element method in structural mechanics
Finite_element_method_in_structural_mechanics
Method in statistics
where hr is the rth element of h(B) and Bi is the ith element of B. When g′(θ) = 0 the delta method cannot be applied. However, if g′′(θ) exists
Delta_method
Granular material interaction simulation technique
The extended discrete element method (XDEM) is a numerical technique that extends the dynamics of granular material or particles as described through the
Extended discrete element method
Extended_discrete_element_method
supraconvergent method is one which converges faster than generally expected (superconvergence or supraconvergence). For example, in the finite element method approximation
Superconvergence
Algorithm for linear programming
polytope is defined by the constraints applied to the objective function. George Dantzig worked on planning methods for the US Army Air Force during World
Simplex_algorithm
Chemical element with atomic number 5 (B)
Boron is a chemical element; it has symbol B and atomic number 5. In its crystalline form it is a brittle, dark, lustrous metalloid; in its amorphous
Boron
Family of implicit and explicit iterative methods
Runge–Kutta methods (English: /ˈrʊŋəˈkʊtɑː/ RUUNG-ə-KUUT-tah) are a family of implicit and explicit iterative methods, which include the Euler method, used
Runge–Kutta_methods
Chemical element with atomic number 91 (Pa)
Protactinium is a chemical element; it has symbol Pa and atomic number 91. It is a dense, radioactive, silvery-gray actinide metal which readily reacts
Protactinium
In applied mathematics, Loubignac iteration is an iterative method in finite element methods. It gives continuous stress field. It is named after Gilles
Loubignac_iteration
Method for representing and evaluating partial differential equations
volume methods can be compared and contrasted with the finite difference methods, which approximate derivatives using nodal values, or finite element methods
Finite_volume_method
Methods of calculating definite integrals
evaluate the integral. For instance, the standard fourth-order Runge–Kutta method applied to the differential equation yields Simpson's rule from above. The differential
Numerical_integration
Structural analysis technique; implementation of the finite element method
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
Direct_stiffness_method
Class of methods used in numerical analysis and scientific computing to solve ODE/PDE
Spectral methods are a class of techniques used in applied mathematics and scientific computing to numerically solve certain differential equations. The
Spectral_method
Method for analyzing stability of slopes of soil or rock
the most commonly applied numerical approach to rock slope analysis and following variations of the DEM exist: distinct-element method Discontinuous Deformation
Slope_stability_analysis
Methods of mathematical approximation
Eigenvalue perturbation Homotopy perturbation method Interval finite element Lyapunov stability Method of dominant balance Order of approximation Perturbation
Perturbation_theory
Methods used to find numerical solutions of ordinary differential equations
Numerical methods for ordinary differential equations are methods used to find numerical approximations to the solutions of ordinary differential equations
Numerical methods for ordinary differential equations
Numerical_methods_for_ordinary_differential_equations
Method of solving differential equations
Multigrid methods can be applied in combination with any of the common discretization techniques. For example, the finite element method may be recast
Multigrid_method
Spanish mechanical engineer
(2004). "Combination of discrete and finite element methods in forming processes". Computer Methods in Applied Mechanics and Engineering. 193 (6–8): 3087–3128
Eugenio_Oñate
Analysis and solving of problems that involve fluid flows
Discrete element method Fictitious domain method Finite element method Finite volume method for unsteady flow Fluid animation Immersed boundary method Lattice
Computational_fluid_dynamics
Lemma in numerical analysis of differential equations
is an important tool for proving error estimates for the finite element method applied to elliptic partial differential equations. Let V {\displaystyle
Céa's_lemma
Type of constraint on solutions to differential equations
differential equations in one dimension: Finite element models". An Introduction to the Finite Element Method (3rd ed.). Boston: McGraw-Hill. p. 110. ISBN 978-0-07-126761-8
Dirichlet_boundary_condition
Syntactic metadata for Java source code
at runtime via reflection. @Target({ElementType.METHOD}) // This annotation can only be applied to class methods. public @interface Tweezable {} The compiler
Java_annotation
Type of differential equation
element method, discontinuous Galerkin finite element method (DGFEM), element-free Galerkin method (EFGM), interpolating element-free Galerkin method
Partial_differential_equation
Numerical method for solving certain differential equations
(1888–1937). It falls within the class of finite element methods. The hybrid Trefftz finite-element method has been considerably advanced since its introduction
Trefftz_method
Numerical optimization algorithm
multidimensional space. It is a direct search method (based on function comparison) and is often applied to nonlinear optimization problems for which derivatives
Nelder–Mead_method
Probabilistic problem-solving algorithm
cryptography. They have also been applied to social sciences, such as sociology, psychology, and political science. Monte Carlo methods have been recognized as
Monte_Carlo_method
American engineer
Interdisciplinary applied mathematics, Volume 7: Computational inelasticity, New York: Springer, 1998. Thomas J. R. Hughes, The Finite Element Method: Linear Static
Thomas_J.R._Hughes
Differential equations involving stochastic processes
methods for solving stochastic differential equations include the Euler–Maruyama method, Milstein method, Runge–Kutta method (SDE), Rosenbrock method
Stochastic differential equation
Stochastic_differential_equation
Algorithm for shuffling a finite sequence
the permutation incrementally as needed. The naïve method of swapping each element with another element chosen randomly from all elements is biased. Different
Fisher–Yates_shuffle
Initial estimate or framework to the solution of a mathematical problem
find. It has been demonstrated that machine learning techniques can be applied to provide initial estimates similar to those invented by humans and to
Ansatz
Calculation of structural loads
differential equation. The finite element method is perhaps the most restrictive and most useful at the same time. This method itself relies upon other structural
Structural_analysis
Simplification of a physical system into a network of discrete components
electromagnetic waves across the lumped element. The first two assumptions result in Kirchhoff's circuit laws when applied to Maxwell's equations and are only
Lumped-element_model
Chemical substance not composed of simpler ones
A chemical element is a species of atom defined by its number of protons. The number of protons is called the atomic number of that element. For example
Chemical_element
Numerical technique
single source. The FMM has also been applied in accelerating the iterative solver in the method of moments (MoM) as applied to computational electromagnetics
Fast_multipole_method
Chemical element with atomic number 118 (Og)
Oganesson is a synthetic chemical element; it has symbol Og and atomic number 118. It was first synthesized in 2002 at the Joint Institute for Nuclear
Oganesson
Numerical technique for bioelectromagnetic modeling
The charge-based formulation of the boundary element method (BEM) is a dimensionality reduction numerical technique that is used to model quasistatic electromagnetic
Charge based boundary element fast multipole method
Charge_based_boundary_element_fast_multipole_method
Type of boundary condition in mathematics
Modeling in Hydrogeochemical Systems. Springer. J. E. Akin (2005). Finite Element Analysis with Error Estimators: An Introduction to the FEM and Adaptive
Robin_boundary_condition
Type of problem involving ODEs or PDEs
Mathematics, EMS Press, 2001 [1994] "Boundary value problem, complex-variable methods", Encyclopedia of Mathematics, EMS Press, 2001 [1994] Linear Partial Differential
Boundary_value_problem
Physical theory with fields invariant under the action of local "gauge" Lie groups
given gauge theory also forms a group, the gauge group of the theory. An element of the gauge group can be parameterized by a smoothly varying function
Gauge_theory
Higher Studying Field
the analysis: the energy methods, flexibility method or direct stiffness method which later developed into finite element method and the plastic analysis
Structural_mechanics
Numerical solution method of computational electromagnetics
frequency-domain finite-difference methods, the title seems to mostly describe the method as applied to scattering problems. The method shares many similarities
Finite-difference frequency-domain method
Finite-difference_frequency-domain_method
Chemical element with atomic number 80 (Hg)
Mercury is a chemical element; it has symbol Hg and atomic number 80. It is commonly known as quicksilver. A heavy, silvery d-block element, mercury is the
Mercury_(element)
Type of ordinary differential equation
obtained by removing the constant term. The term homogeneous was first applied to differential equations by Johann Bernoulli in section 9 of his 1726
Homogeneous differential equation
Homogeneous_differential_equation
Periodic table of the elements with eight or more periods
there is a period 9. The International Union of Pure and Applied Chemistry (IUPAC) defines an element to exist if its lifetime is longer than 10−14 seconds
Extended_periodic_table
Numerical method for solving partial differential equations
finite element method is a numerical method for solving partial differential equations. It is a discretization strategy in which the finite element mesh
P-FEM
Branch of mathematics
mathematics that studies functions, spaces, and operators through quantitative methods of approximation and convergence. It grew out of calculus, especially the
Mathematical_analysis
Solution method for linear differential equations
In mathematical physics, the WKB approximation or WKB method is a technique for finding approximate solutions to linear differential equations with spatially
WKB_approximation
Mathematical approach to quantum physics
evaluated for large-expansion parameters, most efficiently by the variational method. In practice, convergent perturbation expansions often converge slowly while
Perturbation theory (quantum mechanics)
Perturbation_theory_(quantum_mechanics)
Individual component of an HTML document
An HTML element is a type of HTML (HyperText Markup Language) document component, one of several types of HTML nodes (some common node types include document
HTML_element
Branch of physics
modeled by finite element methods); matrix products (when using transfer matrix methods); calculating numerical integrals (when using the method of moments);
Computational electromagnetics
Computational_electromagnetics
Swedish mathematician
Technology with thesis Convergence of the streamline diffusion finite element method for conservation laws under the supervision of Claes Johnson. Szepessy
Anders_Szepessy
Computational method for solving partial differential equations
complicated than the finite element method. Another advantage is it works well on multi variable problems. The finite element method is complicated when working
Kansa_method
particular numerical analysis, the FETI method (finite element tearing and interconnect) is an iterative substructuring method for solving systems of linear equations
FETI
later in Stoke-upon-Trent but the method was modified to yield alloys rather than pure aluminium. Bradley applied for a patent in 1883; due to his broad
History_of_aluminium
Chemical element with atomic number 105 (Db)
Dubnium is a synthetic chemical element; it has symbol Db and atomic number 105. It is highly radioactive: the most stable known isotope, dubnium-268
Dubnium
Branch of ordinary differential equations
to a traditional linear system with constant, real coefficients. When applied to physical systems with periodic potentials, such as crystals in condensed
Floquet_theory
Chemical elements with atomic numbers from 104 to 120
be satisfied for the discovery of a new chemical element to be recognized" (PDF). Pure and Applied Chemistry. 63 (6): 883. doi:10.1351/pac199163060879
Superheavy_element
Interplay between observation, experiment, and theory in science
The scientific method is an empirical method for acquiring knowledge through careful observation, rigorous skepticism, hypothesis testing, and experimental
Scientific_method
Type of functional equation (mathematics)
and sent the solution to Euler. Both further developed Lagrange's method and applied it to mechanics, which led to the formulation of Lagrangian mechanics
Differential_equation
Formal method for the development of computer-based systems
The Vienna Development Method (VDM) is one of the longest-established formal methods for the development of computer-based systems. Originating in work
Vienna_Development_Method
American academic (born 1945)
for his contributions to the finite element method, solid mechanics, plate theory, composite materials, and applied mathematics. Reddy has published over
J._N._Reddy_(engineer)
Methods in numerical analysis not requiring knowledge of neighboring points
the velocity field. Numerical methods such as the finite difference method, finite-volume method, and finite element method were originally defined on meshes
Meshfree_methods
Space of all possible states that a system can take
in Hamiltonian optics. In medicine and bioengineering, the phase space method is used to visualize multidimensional physiological responses. Configuration
Phase_space
Existence and uniqueness of solutions to initial value problems
successive approximations. In this context, this fixed-point iteration method is known as Picard iteration. Set φ 0 ( t ) = y 0 {\displaystyle \varphi
Picard–Lindelöf_theorem
Chemical element with atomic number 117 (Ts)
Tennessine is a synthetic element; it has symbol Ts and atomic number 117. It has the second-highest atomic number, the joint-highest atomic mass of all
Tennessine
Method for numerical differential equations
in this case a nonconforming method for the approximation of (2), which includes the nonconforming finite element method. Note that the converse is not
Gradient discretisation method
Gradient_discretisation_method
Factors that influence engineering design process
quality. It can also calculate stress and displacement using the finite element method to determine stresses throughout the part. The production planning and
Engineering_design_process
Operation that extracts small elements and details from given images
would not be extracted by only utilizing threshold method. In this case, before Otsu's method is applied to input image, white top-hat transform should be
Top-hat_transform
Formulation of classical mechanics using momenta
Poisson algebra (equipped with some suitable topology) such that for any element A of the algebra, A2 maps to a nonnegative real number. A further generalization
Hamiltonian_mechanics
Element whose atomic number is greater than 92
the element joliotium (Jl) after Frédéric Joliot-Curie (1965). IUPAC concluded that the JINR had been the first to convincingly synthesize the element (1965)
Transuranium_element
Finite difference method for numerically solving parabolic differential equations
{\displaystyle N} indicates the matrix size. The Crank–Nicolson method is often applied to diffusion problems. As an example, for linear diffusion, ∂ u
Crank–Nicolson_method
Differential equation that is linear with respect to the unknown function
same in each term), then the method of undetermined coefficients may be used. Still more general, the annihilator method applies when f satisfies a homogeneous
Linear_differential_equation
Determinant of the matrix of first derivatives of a set of functions
{y'_{2}}{y_{2}}}y_{1}=-W(x)/y_{2}} and can be solved exactly (at least in theory). The method is easily generalized to higher order equations. The relationship between
Wronskian
APPLIED ELEMENT-METHOD
APPLIED ELEMENT-METHOD
Male
Italian
 Italian, Portuguese and Spanish form of Latin Clementius, CLEMENTE means "gentle and merciful."
Male
English
English surname transferred to forename use, derived from Latin Clemens or Clement, CLEMENTS means "gentle and merciful."
Surname or Lastname
English
English : from Middle English appel ‘apple’ (Old English æppel), acquired as a surname in any of various senses: a topographic name for someone living by an apple orchard; an occupational name for a grower or seller of apples; or a nickname for someone supposed to resemble an apple in some way, e.g. in having bright red cheeks. The economic importance in medieval northern Europe of apples, as a fruit that could be grown in a cold climate and would keep for use throughout the winter, is hard to appreciate in these days of rapid transportation and year-round availability of fruits of all kind.Americanized form of Appel or Apfel.
Boy/Male
English
Gentle. Famous Bearer: Clement Moore, writer of 'Twas the Night Before Christmas'.
Male
Slovene
Slovene form of Greek Klementos, KLEMEN means "gentle and merciful."
Male
English
Short form of Latin Clementius, CLEMENT means "gentle and merciful." meaning "gentle and merciful." In the bible, this is the name of a companion of Paul.
Boy/Male
Australian, British, Danish, Dutch, English, Finnish, French, German, Irish, Latin, Swedish
Gentle; Merciful; Mild; Form of Clement
Boy/Male
African, American, Australian, British, Chinese, Christian, Danish, English, French, German, Greek, Indian, Jamaican, Latin, Swedish, Swiss
Merciful; Mild; Gentle; Giving Mercy; Merciful in French
Biblical
mild; good; merciful
Male
Polish
 Danish, German, Polish and Swedish form of Greek Klementos, KLEMENS means "gentle and merciful."
Surname or Lastname
English
English : patronymic from the personal name Clement.German, Dutch, and Danish : from the personal name Clemens (see Clement).Samuel Langhorne Clemens, better known by his pen name, Mark Twain, was descended from VA stock on his father’s side, from a Robert Clemens, who was born in Warwickshire, England, in 1634.
Male
Russian
(Климент) Russian form of Greek Klementos, KLIMENT means "gentle and merciful."
Boy/Male
English
Gentle. Famous Bearer: Clement Moore, writer of 'Twas the Night Before Christmas'.
Surname or Lastname
English, French, and Dutch
English, French, and Dutch : from the Latin personal name Clemens meaning ‘merciful’ (genitive Clementis). This achieved popularity firstly through having been borne by an early saint who was a disciple of St. Paul, and later because it was selected as a symbolic name by a number of early popes. There has also been some confusion with the personal name Clemence (Latin Clementia, meaning ‘mercy’, an abstract noun derived from the adjective; in part a masculine name from Latin Clementius, a later derivative of Clemens). As an American family name, Clement has absorbed cognates in other continental European languages. (For forms, see Hanks and Hodges 1988.)
Male
Hungarian
Hungarian form of Greek Klementos, KELEMEN means "gentle and merciful."
Boy/Male
English American Biblical Latin
Gentle. Famous Bearer: Clement Moore, writer of 'Twas the Night Before Christmas'.
Surname or Lastname
English
English : patronymic from the personal name Clement. As an American family name, this form has absorbed cognates in other continental European languages. (For forms, see Hanks and Hodges 1988.)
Boy/Male
English American Danish
Gentle. Famous Bearer: Clement Moore, writer of 'Twas the Night Before Christmas'.
Boy/Male
Czechoslovakian, Danish, German, Greek, Latin, Polish
Giving Mercy; Mild; Merciful
Surname or Lastname
English
English : variant of Appling.
APPLIED ELEMENT-METHOD
APPLIED ELEMENT-METHOD
Girl/Female
Muslim
Victorious
Boy/Male
American, British, English, French
Mild Strength
Boy/Male
Biblical
The beatitude of God.
Surname or Lastname
English
English : habitational name from any of the places so called, in Cheshire, Hampshire, and Staffordshire. These are all named in Old English as cyningeslēah ‘the woodland clearing (Old English lēah) of the king (cyning)’.
Boy/Male
American, Arabic, Christian, Danish, Gaelic, Gujarati, Hindu, Indian, Muslim, Parsi, Persian, Punjabi, Telugu
Kings; Royal; Ancient; Distant; Lord Krishna
Girl/Female
Latin
Blessed.
Surname or Lastname
English
English : variant spelling of Ayer.
Biblical
a lamb; sleeping
Female
Hebrew
Variant spelling of Hebrew Yeruwsha, YERUSHA means "dispossessor" or "possessed (by a husband)."
Female
Croatian
, a small mountain.
APPLIED ELEMENT-METHOD
APPLIED ELEMENT-METHOD
APPLIED ELEMENT-METHOD
APPLIED ELEMENT-METHOD
APPLIED ELEMENT-METHOD
a.
Next after the tenth; as, the eleventh chapter.
n.
Sometimes a curve, or surface, or volume is considered as described by a moving point, or curve, or surface, the latter being at any instant called an element of the former.
n.
The four elements were, air, earth, water, and fire
n.
An infinitesimal part of anything of the same nature as the entire magnitude considered; as, in a solid an element may be the infinitesimal portion between any two planes that are separated an indefinitely small distance. In the calculus, element is sometimes used as synonymous with differential.
n.
To overlay or coat with cement; as, to cement a cellar bottom.
n.
One out of several parts combined in a system of aggregation, when each is of the nature of the whole; as, a single cell is an element of the honeycomb.
v. t.
To compound of elements or first principles.
n.
The quotient of a unit divided by eleven; one of eleven equal parts.
v. i.
To grow like an apple; to bear apples.
a.
Constituting one of eleven parts into which a thing is divided; as, the eleventh part of a thing.
n.
One of the ultimate, undecomposable constituents of any kind of matter. Specifically: (Chem.) A substance which cannot be decomposed into different kinds of matter by any means at present employed; as, the elements of water are oxygen and hydrogen.
n.
The elements of the alchemists were salt, sulphur, and mercury.
n.
One of the ultimate parts which are variously combined in anything; as, letters are the elements of written language; hence, also, a simple portion of that which is complex, as a shaft, lever, wheel, or any simple part in a machine; one of the essential ingredients of any mixture; a constituent part; as, quartz, feldspar, and mica are the elements of granite.
n.
The simplest or fundamental principles of any system in philosophy, science, or art; rudiments; as, the elements of geometry, or of music.
n.
He who, or that which, applies.
a.
Pertaining to the elements, first principles, and primary ingredients, or to the four supposed elements of the material world; as, elemental air.
a.
Acting with great force; furious; violent; impetuous; forcible; mighty; as, vehement wind; a vehement torrent; a vehement fire or heat.
n.
One of the necessary data or values upon which a system of calculations depends, or general conclusions are based; as, the elements of a planet's orbit.
v. t.
To constitute; to make up with elements.
n.
Any outline or sketch, regarded as containing the fundamental ideas or features of the thing in question; as, the elements of a plan.