Search results
Results from the WOW.Com Content Network
Cubic materials are special orthotropic materials that are invariant with respect to 90° rotations with respect to the principal axes, i.e., the material is the same along its principal axes. Due to these additional symmetries the stiffness tensor can be written with just three different material properties like
Monoclinic crystal An example of the monoclinic crystal orthoclase. In crystallography, the monoclinic crystal system is one of the seven crystal systems. A crystal system is described by three vectors. In the monoclinic system, the crystal is described by vectors of unequal lengths, as in the orthorhombic system. They form a parallelogram ...
The full stiffness matrix A is the sum of the element stiffness matrices. In particular, for basis functions that are only supported locally, the stiffness matrix is sparse. For many standard choices of basis functions, i.e. piecewise linear basis functions on triangles, there are simple formulas for the element stiffness matrices.
Wood is an example of an orthotropic material. Material properties in three perpendicular directions (axial, radial, and circumferential) are different. In material science and solid mechanics, orthotropic materials have material properties at a particular point which differ along three orthogonal axes, where each axis has twofold rotational ...
= system stiffness matrix, which is the collective effect of the individual elements' stiffness matrices :. r {\displaystyle \mathbf {r} } = vector of the system's nodal displacements. R o {\displaystyle \mathbf {R} ^{o}} = vector of equivalent nodal forces, representing all external effects other than the nodal forces which are already ...
Elastic constants are specific parameters that quantify the stiffness of a material in response to applied stresses and are fundamental in defining the elastic properties of materials. These constants form the elements of the stiffness matrix in tensor notation, which relates stress to strain through linear equations in anisotropic materials.
The elasticity tensor is a fourth-rank tensor describing the stress-strain relation in a linear elastic material. [ 1 ] [ 2 ] Other names are elastic modulus tensor and stiffness tensor . Common symbols include C {\displaystyle \mathbf {C} } and Y {\displaystyle \mathbf {Y} } .
The direct stiffness method originated in the field of aerospace. Researchers looked at various approaches for analysis of complex airplane frames. These included elasticity theory, energy principles in structural mechanics, flexibility method and matrix stiffness method. It was through analysis of these methods that the direct stiffness method ...