Concepts inInteractive surface modeling using modal analysis
Surface
In mathematics, specifically in topology, a surface is a two-dimensional topological manifold. The most familiar examples are those that arise as the boundaries of solid objects in ordinary three-dimensional Euclidean space R ¿ for example, the surface of a ball. On the other hand, there are surfaces, such as the Klein bottle, that cannot be embedded in three-dimensional Euclidean space without introducing singularities or self-intersections.
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Modal analysis
Modal analysis is the study of the dynamic properties of structures under vibrational excitation. Modal analysis is the field of measuring and analysing the dynamic response of structures and or fluids when excited by an input. Examples would include measuring the vibration of a car's body when it is attached to an electromagnetic shaker, or the noise pattern in a room when excited by a loudspeaker.
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Nonlinear programming
In mathematics, nonlinear programming (NLP) is the process of solving a system of equalities and inequalities, collectively termed constraints, over a set of unknown real variables, along with an objective function to be maximized or minimized, where some of the constraints or the objective function are nonlinear.
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Quasi-Newton method
In optimization, quasi-Newton methods (a special case of variable metric methods) are algorithms for finding local maxima and minima of functions. Quasi-Newton methods are based on Newton's method to find the stationary point of a function, where the gradient is 0. Newton's method assumes that the function can be locally approximated as a quadratic in the region around the optimum, and uses the first and second derivatives to find the stationary point.
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Deformation (engineering)
In materials science, deformation is a change in the shape or size of an object due to an applied force (the deformation energy in this case is transferred through work) or a change in temperature (the deformation energy in this case is transferred through heat). The first case can be a result of tensile (pulling) forces, compressive (pushing) forces, shear, bending or torsion (twisting).
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Elasticity (physics)
In physics, elasticity is a physical property of materials which return to their original shape after the stress that caused their deformation is no longer applied.
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Force
In physics, a force is any influence that causes an object to undergo a certain change, either concerning its movement, direction, or geometrical construction. In other words, a force is that which can cause an object with mass to change its velocity (which includes to begin moving from a state of rest), i.e. , to accelerate, or which can cause a flexible object to deform. Force can also be described by intuitive concepts such as a push or pull.
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Candidate solution
In optimization (a branch of mathematics) and search algorithms (a topic in computer science), a candidate solution is a member of a set of possible solutions to a given problem. A candidate solution does not have to be a likely or reasonable solution to the problem ¿ it is simply in the set that satisfies all constraints. The space of all candidate solutions is called the feasible region, feasible set, search space, or solution space.
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