What is the difference between lumped mass matrix and consistent mass matrix?
The consistent mass matrix is fully populated whereas lumped mass matrix is diagonal. Stiffness matrix: The stiffness matrix [k] is symmetric. The total stiffness matrix will be formed by assembling all the elements together to form a structure.
What are the two types of mass matrix?
Lumped and.
What is lumped mass structural dynamics?
Structural Dynamics. Lumped mass systems – masses can be assumed to be concentrated at specific locations, and to be connected by massless elements such as springs. Very useful for buildings where most of mass is at (or attached to) floors. Newton’s law is expressed in terms of absolute velocity and acceleration, üt(t) …
What is lumped matrix?
Lumped Mass Matrix: It is a diagonal matrix obtained by either row or column sum lumping schemes commonly used in literature [3] . It presents a computational advantage especially in the problems of impact /crash analysis the procedure as involves then a mass matrix inversion.
Why do we need a Jacobian matrix in the finite element method?
Why do we need a Jacobian matrix in the finite element method? D : The Jacobian matrix is required to map the natural coordinate system to the cartesian coordinate system. Answer:-D : The Jacobian matrix is required to map the natural coordinate system to the cartesian coordinate system.
What is lumped mass?
A lumped mass is a load that can be applied to a node in a static stress, natural frequency (modal) or modal superposition analysis. A lumped mass can be used to resist the translation or rotation of a node.
What is the other name of stiffness method?
the displacement method
Another name for the method is the force method because forces are the unknown quantities in equations of compatibility. Stiffness Method In the stiffness method, displacements (rather than forces) are taken as the unknown quantities. For this reason, the method is also called the displacement method.
What does lumped mass mean?
What is difference between stiffness and flexibility matrix method?
When comparing the flexibility and stiffness methods, it is seen that the flexibility method requires the solution of equations of compatibility for unknown forces whereas the stiffness method requires the solution of equations of equilibrium for unknown displacements.
Is stiffness matrix a tensor?
Stiffness is the derivative of stress with respect to strain. When stress and strain are represented as vectors, stiffness is a second or- der tensor, or matrix.
What is Jacobian matrix used for?
The Jacobian matrix is used to analyze the small signal stability of the system. The equilibrium point Xo is calculated by solving the equation f(Xo,Uo) = 0. This Jacobian matrix is derived from the state matrix and the elements of this Jacobian matrix will be used to perform sensitivity result.
What is warpage in FEA?
Warpage – It is defined as angle between normals to two planes formed by splitting the quad element along diagonals. Max. angle out of the two possibilities is reported as warp angle. you can also say it as, in any quad element one node out of four is out of plane.
How do you find the lumped mass matrix?
The mass matrix formed in this way is called as lumped mass matrix. [M]=ρAhe2[ 1000 0000 0010 0000] for a beam element.
What is the difference between flexibility and stiffness method?
Why stiffness method is preferred?
The Stiffness method provides a very systematic way of analyzing determinate and indeterminate structures. These LOCAL (member) force-displacement relationships can be easily established for ALL the members in the truss, simply by using given material and geometric properties of the different members.
What is meant by consistent and lumped mass strategy?
Also, we have used the same shape function for computing both mass and stiffness matrices. Hence, these mass matrices are called as consistent matrices. We distribute the complete mass of the element at the two nodes. The mass matrix formed in this way is called as lumped mass matrix.
What is meant by lumped mass?
What is base shear?
Base shear is an estimate of the maximum expected lateral force on the base of the structure due to seismic activity. It is calculated using the seismic zone, soil material, and building code lateral force equations (Figure 10.3). Notations in IBC/UBC are used in mathematical equations. Figure 10.3.