a = index referring to the lumped mass ‘a’ b = index referring to the lumped mass ‘b’ Fxi = X component of the inertial force acting on the i-th lumped mass (i = a or b) Fyi = Y component of the inertial force acting on the i-th lumped mass (i = a or b) Fzi = Z component of the inertial force acting on the i-th lumped mass (i = a or b) R = half of the distance between the two arms (bars) in par...

In the present work the pull-in voltage of a micro cracked cantilever beam subjected to nonlinear electrostatic pressure was studied. Two mathematical models were employed for modeling the problem: a lumped mass model and a classical beam model. The effect of crack in the lumped mass model is the reduction of the effective stiffness of the beam and in the beam model; the crack is modeled as a m...

An analytical approach is presented to assess the response of offshore structures under seismic excitation. This paper evaluates the impacts of different fluid field models and the mass of equipment at the top of offshore structure which is simulated as lumped mass on the responses of offshore structures. To do this, two and three dimensional fluid field models are developed. In three dimension...

Elevated tanks are important structures in storing vital products, such as petroleum products for cities and industrial facilities, as well as water storage. These structures have various types and are constructed in a way that a greater portion of their weight is concentrated at an elevation much about the base. Damage to these structures during strong ground motions may lead to fire or other ...

Abstract When solving the wave equation with finite elements, mass lumping allows for explicit time stepping, avoiding cost of a lower-upper decomposition large sparse matrix. Mass on reference element amounts to numerical quadrature. The weights should be positive stable stepping and preserve accuracy. standard triangular polynomial except linear element, do not have these properties. Accuracy...

elevated tanks are important structures in storing vital products, such as petroleum products for cities and industrial facilities, as well as water storage. these structures have various types and are constructed in a way that a greater portion of their weight is concentrated at an elevation much about the base. damage to these structures during strong ground motions may lead to fire or other ...

Elevated tanks are very important structures and consist of various types. Water supply is vital to control fires during earthquakes. Also they are utilized to store different products, like petroleum supplies in cities and industrial zones. Damage to these structures during strong ground motions may lead to fire or other hazardous events. Elevated tanks should stay functional after and before ...

We study the spatially semidiscrete lumped mass method for the model homogeneous heat equation with homogeneous Dirichlet boundary conditions. Improving earlier results we show that known optimal order smooth initial data error estimates for the standard Galerkin method carry over to the lumped mass method whereas nonsmooth initial data estimates require special assumptions on the triangulation...

elevated tanks are very important structures and consist of various types. water supply is vital to control fires during earthquakes. also they are utilized to store different products, like petroleum supplies in cities and industrial zones. damage to these structures during strong ground motions may lead to fire or other hazardous events. elevated tanks should stay functional after and before ...