A mixed finite element for the nonlinear analysis of in‐plane loaded masonry walls

Abstract

Summary A mixed membrane eight‐node quadrilateral finite element for the analysis of masonry walls is presented. Assuming that a nonlinear and history‐dependent 2D stress‐strain constitutive law is used to model masonry material, the element derivation is based on a Hu‐Washizu variational statement, involving displacement, strain, and stress fields as primary variables. As the behavior of masonry structures is often characterized by strain localization phenomena, due to strain softening at material level, a discontinuous, piecewise constant interpolation of the strain field is considered at element level, to capture highly nonlinear strain spatial distributions also within finite elements. Newton's method of solution is adopted for the element state determination problem. For avoiding pathological sensitivity to the finite element mesh, a novel algorithm is proposed to perform an integral‐type nonlocal regularization of the constitutive equations in the present mixed formulation. By the comparison with competing serendipity displacement‐based formulation, numerical simulations prove high performances of the proposed finite element, especially when coarse meshes are adopted.

A dual decomposition of the closest point projection in incremental elasto‐plasticity using a mixed shell finite element

“…It is worth noting that the proposed decomposed formulation furnishes the same discrete equations as in other works [39][40][41] which formalize, within a Hu-Washizu variational formulation, an initial proposal for reinforced concrete frames using equilibrated mixed beam FEs. 42 The strategy proposed in this work exhibits good numerical performance and can be implemented in existing FE codes.…”

Lower-Bound Limit Analysis of Masonry Arches with Multiple Failure Sections

“…The structural analysis of masonry structures plays a critical role in the effort to preserve and restore architectural heritage and historical buildings. Many computational approaches have been developed for addressing such a task, at different scales and levels of complexity, including micromechanical approaches (e.g., see [1,2]), multiscale/homogenization approaches (e.g., see [3][4][5][6]) and macromechanical/phenomenological approaches (e.g., see [7][8][9][10][11]), to be used in finite element formulations for inelastic structures (e.g., see [12][13][14][15][16][17][18]). As an alternative strategy, whose roots trace back to the first discovery by Robert Hook of the analogy between the structural behavior of a masonry arch and that of a catenary, the structural capacity can be computed by a limit analysis approach (e.g., see [19,20]).…”

An efficient isostatic mixed shell element for coarse mesh solution

“…Moreover, mixed FE are diffusely employed for the analysis of structures undergoing physical nonlinearities. [19][20][21] An interesting framework for developing mixed FE is the Trefftz method. 22 This method is based on assuming stress interpolations that a priori simultaneously satisfy both equilibrium and compatibility equations.…”

“…Recent formulations of mixed FE can be found in References 17,18. Moreover, mixed FE are diffusely employed for the analysis of structures undergoing physical nonlinearities 19‐21 …”