algebraic frames are generalizations of fourier transforms on locally compact abelian groups in the sense that the family of vectors forming the frame are replaced by a family of unbounded linear functionals. the paper studies the indexing measure space of the algebraic frames; as the investigation narrows down to the class of lower semiframes, more relations are revealed between the discret...

by minimizing the total potential energy function and deploying the virtual work principle, a higher-order stiffness matrix is achieved. this new tangent stiffness matrix is used to solve the frame with geometric nonlinear behavior. since authors’ formulation takes into account the higher-order terms of the strain vector, the convergence speed of the solution process will increase. in fact, bot...

there are several methods for analysing the behaviour of underground structures under different loading conditions. most of these methods have many simplifications; therefore, in some cases, the results are too conservative and a very high safety factor, usually of more than 2 is needed. on the other hand, for stability analysis and the designing of support systems, these methods consider segme...

progressive collapse is a chain reaction of failures propagating throughout a portion of the structure disproportionate to the original local failure occurring when a sudden loss of a critical load‐bearing element initiates a structural element failure, eventually resulting in partial or full collapse of the structure. both general services administration (gsa) and united states department of d...

By minimizing the total potential energy function and deploying the virtual work principle, a higher-order stiffness matrix is achieved. This new tangent stiffness matrix is used to solve the frame with geometric nonlinear behavior. Since authors’ formulation takes into account the higher-order terms of the strain vector, the convergence speed of the solution process will increase. In fac...