High strength steel sheets, widely used in industrial applications, exhibit a significant anisotr... more High strength steel sheets, widely used in industrial applications, exhibit a significant anisotropy of plastic response between their rolling and transverse direction. Hills yield criterion is the most popular in sheet metal forming FE simulations, because its parameters are easily determined. In the literature, several other criteria are proposed that can better describe the anisotropic behavior of specific materials. In limit analysis the material elastic properties are irrelevant. A formulation, based on the static theorem, requires only the equations of equilibrium and a respective yield criterion to describe the safety margins of a structure. Limit analysis implements standard FEM data into mathematical optimization packages to yield the respective safety factor. Depending on the yield criterion type, a large scale nonlinear mathematical programming problem must be solved. Quadratic yield criteria, like Hill, lead to Second Order Cone Programming problems. Non-quadratic yield ...
Shakedown analysis, currently implemented by the coupling of FEM with optimization techniques, de... more Shakedown analysis, currently implemented by the coupling of FEM with optimization techniques, defines safe limit states of ductile structures subjected to arbitrarily varying loads. In the present study, the selective algorithm, a method to enhance computational efficiency, is combined with a general non-linear optimization package and several criteria for active region selection are compared. Moreover a new criterion based on Lagrange multipliers and a way to efficiently enlarge the most active region is presented.
Limit analysis (LA) of spatial metal frames is currently implemented by the coupling of Finite El... more Limit analysis (LA) of spatial metal frames is currently implemented by the coupling of Finite Element Methods (FEM) with techniques of computational optimization. If the involved yield criteria are linear or piecewise linearized the optimization problem becomes a linear programming (LP) problem, for which free and commercial software packages are available. Otherwise, under non-linear yield criteria a non-linear programming (NLP) problem must be solved. The algorithms deployed for the last depend on the non-linearity type of the criteria. Nowadays, the mathematical programming research community has developed excellent algorithms for optimization under ellipsoidal inequalities, capable of treating efficiently even large-scale problems. In the present research, non-linear mathematical programming techniques are used in the construction of inner and outer ellipsoidal approximations to the yield criteria for aluminum hollow sections according to Eurocode 9. Examples of limit analysis ...
Standard Pushover Analysis (SPA), described in several codes (EC8, FEMA 356, ATC 40) is using loa... more Standard Pushover Analysis (SPA), described in several codes (EC8, FEMA 356, ATC 40) is using loads that try to simulate earthquake inertia forces over the masses of the structure, using just the first eigenmode. Various methods were developed in the literature to cover SPA inherent weakness to predict the non-linear behavior of structures with significant higher mode effects. Based on Shakedown analysis (SA) Bisbos and Ampatzis developed a technique for the assessment of seismic behavior of elastoplastic framed steel structures, taking into account higher mode effects. The Shakedown locus, a design tool obtained by parametric SA, is used as the desirable generalized yield criterion for the whole of a structure under variable loading. Further elaboration of the locus, results in the identification of the critical load paths, essentially defining load combinations in the equivalent earthquake forces' space. These critical combinations are qualified as the reference loading to be ...
Limit and shakedown analysis problems of Computational Mechanics lead to convex optimization prob... more Limit and shakedown analysis problems of Computational Mechanics lead to convex optimization problems, characterized by linear objective functions, linear equality constraints and constraints expressing the restrictions imposed by the material strength. It is shown that two important strength criteria, the Mohr–Coulomb and the Tresca criterion, can be represented as systems of semidefinite constraints, leading this way to semidefinite programming problems.
The present paper deals with the computation of the local contact loads and displacements on a ho... more The present paper deals with the computation of the local contact loads and displacements on a horizontal vessel, loosely resting on saddles, by using Sanders' equations for cylindrical shells with the presence of internal pressure. The boundary nonlinear inequality constraints lead to the formulation of a linear complementarity problem (LCP). This LCP is a direct extension of the force method of structural analysis to the case of debonding. The flexibility coefficients are computed through a Fourier series representation.
The finite element method discretized static shakedown analysis of steel constructions leads to l... more The finite element method discretized static shakedown analysis of steel constructions leads to large, sparse convex optimization problems. Under the von Mises yield criterion, they lead to second-order cone programming problems, for which the most appropriate techniques are Interior Point Methods. Various approaches exploiting the specific characteristics of the shakedown problems are presented and discussed.
High strength steel sheets, widely used in industrial applications, exhibit a significant anisotr... more High strength steel sheets, widely used in industrial applications, exhibit a significant anisotropy of plastic response between their rolling and transverse direction. Hills yield criterion is the most popular in sheet metal forming FE simulations, because its parameters are easily determined. In the literature, several other criteria are proposed that can better describe the anisotropic behavior of specific materials. In limit analysis the material elastic properties are irrelevant. A formulation, based on the static theorem, requires only the equations of equilibrium and a respective yield criterion to describe the safety margins of a structure. Limit analysis implements standard FEM data into mathematical optimization packages to yield the respective safety factor. Depending on the yield criterion type, a large scale nonlinear mathematical programming problem must be solved. Quadratic yield criteria, like Hill, lead to Second Order Cone Programming problems. Non-quadratic yield ...
Shakedown analysis, currently implemented by the coupling of FEM with optimization techniques, de... more Shakedown analysis, currently implemented by the coupling of FEM with optimization techniques, defines safe limit states of ductile structures subjected to arbitrarily varying loads. In the present study, the selective algorithm, a method to enhance computational efficiency, is combined with a general non-linear optimization package and several criteria for active region selection are compared. Moreover a new criterion based on Lagrange multipliers and a way to efficiently enlarge the most active region is presented.
Limit analysis (LA) of spatial metal frames is currently implemented by the coupling of Finite El... more Limit analysis (LA) of spatial metal frames is currently implemented by the coupling of Finite Element Methods (FEM) with techniques of computational optimization. If the involved yield criteria are linear or piecewise linearized the optimization problem becomes a linear programming (LP) problem, for which free and commercial software packages are available. Otherwise, under non-linear yield criteria a non-linear programming (NLP) problem must be solved. The algorithms deployed for the last depend on the non-linearity type of the criteria. Nowadays, the mathematical programming research community has developed excellent algorithms for optimization under ellipsoidal inequalities, capable of treating efficiently even large-scale problems. In the present research, non-linear mathematical programming techniques are used in the construction of inner and outer ellipsoidal approximations to the yield criteria for aluminum hollow sections according to Eurocode 9. Examples of limit analysis ...
Standard Pushover Analysis (SPA), described in several codes (EC8, FEMA 356, ATC 40) is using loa... more Standard Pushover Analysis (SPA), described in several codes (EC8, FEMA 356, ATC 40) is using loads that try to simulate earthquake inertia forces over the masses of the structure, using just the first eigenmode. Various methods were developed in the literature to cover SPA inherent weakness to predict the non-linear behavior of structures with significant higher mode effects. Based on Shakedown analysis (SA) Bisbos and Ampatzis developed a technique for the assessment of seismic behavior of elastoplastic framed steel structures, taking into account higher mode effects. The Shakedown locus, a design tool obtained by parametric SA, is used as the desirable generalized yield criterion for the whole of a structure under variable loading. Further elaboration of the locus, results in the identification of the critical load paths, essentially defining load combinations in the equivalent earthquake forces' space. These critical combinations are qualified as the reference loading to be ...
Limit and shakedown analysis problems of Computational Mechanics lead to convex optimization prob... more Limit and shakedown analysis problems of Computational Mechanics lead to convex optimization problems, characterized by linear objective functions, linear equality constraints and constraints expressing the restrictions imposed by the material strength. It is shown that two important strength criteria, the Mohr–Coulomb and the Tresca criterion, can be represented as systems of semidefinite constraints, leading this way to semidefinite programming problems.
The present paper deals with the computation of the local contact loads and displacements on a ho... more The present paper deals with the computation of the local contact loads and displacements on a horizontal vessel, loosely resting on saddles, by using Sanders' equations for cylindrical shells with the presence of internal pressure. The boundary nonlinear inequality constraints lead to the formulation of a linear complementarity problem (LCP). This LCP is a direct extension of the force method of structural analysis to the case of debonding. The flexibility coefficients are computed through a Fourier series representation.
The finite element method discretized static shakedown analysis of steel constructions leads to l... more The finite element method discretized static shakedown analysis of steel constructions leads to large, sparse convex optimization problems. Under the von Mises yield criterion, they lead to second-order cone programming problems, for which the most appropriate techniques are Interior Point Methods. Various approaches exploiting the specific characteristics of the shakedown problems are presented and discussed.
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Papers by Christos Bisbos