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In a broad sense, the term graphic statics is used to describe the technique of solving particular practical problems of statics using graphical means. [1] Actively used in the architecture of the 19th century, the methods of graphic statics were largely abandoned in the second half of the 20th century, primarily due to widespread use of frame structures of steel and reinforced concrete that ...
An alternative approach, e.g., defining the normal matrix as = of size , takes advantage of the fact that for a given matrix with orthonormal columns the eigenvalue problem of the Rayleigh–Ritz method for the matrix = = can be interpreted as a singular value problem for the matrix . This interpretation allows simple simultaneous calculation ...
The ground vector is the resultant of algebraically adding the air vector and the wind vector. The wind triangle describes the relationships among the quantities used in air navigation. When two of the three vectors, or four of the six components, are known, the remaining quantities can be derived. The three principal types of problems to solve ...
The finite point method (FPM) is a meshfree method for solving partial differential equations (PDEs) on scattered distributions of points. The FPM was proposed in the mid-nineties in (Oñate, Idelsohn, Zienkiewicz & Taylor, 1996a), [1] (Oñate, Idelsohn, Zienkiewicz, Taylor & Sacco, 1996b) [2] and (Oñate & Idelsohn, 1998a) [3] with the purpose to facilitate the solution of problems involving ...
Admissible solutions are then a linear combination of solutions to the generalized eigenvalue problem = where is the eigenvalue and is the (imaginary) angular frequency. The principal vibration modes are different from the principal compliance modes, which are the eigenvectors of k {\displaystyle k} alone.
A good way to estimate the lowest modal vector (), that generally works well for most structures (even though is not guaranteed), is to assume () equal to the static displacement from an applied force that has the same relative distribution of the diagonal mass matrix terms. The latter can be elucidated by the following 3-DOF example.
Figure 1: Parallelogram construction for adding vectors. This construction has the same result as moving F 2 so its tail coincides with the head of F 1, and taking the net force as the vector joining the tail of F 1 to the head of F 2. This procedure can be repeated to add F 3 to the resultant F 1 + F 2, and so forth.
Stress resultants are simplified representations of the stress state in structural elements such as beams, plates, or shells. [1] The geometry of typical structural elements allows the internal stress state to be simplified because of the existence of a "thickness'" direction in which the size of the element is much smaller than in other directions.