{"id":17403,"date":"2024-09-25T15:16:42","date_gmt":"2024-09-25T13:16:42","guid":{"rendered":"https:\/\/navier-lab.fr\/?page_id=17403"},"modified":"2024-11-18T21:56:07","modified_gmt":"2024-11-18T20:56:07","slug":"computational-methods-for-structural-engineering","status":"publish","type":"page","link":"https:\/\/navier-lab.fr\/en\/research\/materiaux-et-structures-architectures-msa\/modelisation-et-changements-dechelle\/computational-methods-for-structural-engineering\/","title":{"rendered":"Structural Analysis"},"content":{"rendered":"

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Our research focuses on designing innovative computational methods tailored for structural calculations in civil engineering, with a particular emphasis on failure analysis. These developments include advanced techniques in numerical limit analysis, damage mechanics, and the modeling of complex materials and structural systems.<\/p>\n

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Numerical limit analysis<\/h2>Read More<\/a><\/div>\n <\/article><\/div><\/div>
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Applications in Civil Engineering Structures<\/h2>Read More<\/a><\/div>\n <\/article><\/div><\/div>
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Fracture and damage in heterogeneous materials<\/h2>Read More<\/a><\/div>\n <\/article><\/div><\/div><\/div><\/div><\/section>
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Numerical Limit Analysis<\/strong><\/h3>\n

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\nJ\u00e9r\u00e9my Bleyer, Ghazi Hassen (ME)
\nColl.: Vincent Lecl\u00e8re (Cermics)
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Limit analysis and yield design theories enable direct estimation of the ultimate load that a structure can withstand, based on the material’s strength properties. These methods provide lower and upper bounds for the load capacity, derived from variational principles applied to stress and displacement. However, their numerical implementation is challenging due to the complex, non-smooth, large-scale convex optimization problems they generate. These problems are categorized under conic programming, for which specialized solvers, such as those using interior-point algorithms, have been developed.<\/p>\n

We are advancing finite-element models for various structural types, including continua, beams, plates, and shells. These models are implemented using the FEniCS finite element library, combined with the Mosek conic programming solver. The automation of these processes is integrated into the open-source package, dolfinx_optim<\/em><\/a>. More recently, we work towards extending such theories to the uncertain\/stochastic cases using robust and stochastic optimization theories.<\/p>\n<\/div>\n

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References\u00a0<\/span><\/h4>\n