Stress-based Element Research Articles

Innovative triangular plate elements for enhanced plate bending analyses

The performance of triangular elements satisfying either compatibility or incompatibility conditions in the plate bending analyses is of great importance. To achieve highly accurate responses, four elements are formulated for the structural analysis in this study. All of these elements have thirteen nodes with different degree-of-freedom arrangements. Two of them are displacement-based compatible triangular elements, which are named Karimi Pour Compatible Triangular (KCT) and Noroozinejad Compatible Triangular (NCT) elements. Besides, the other two stress-based incompatible triangular elements are also suggested with the names of Karimi Pour Incompatible Triangular (KIT) and Noroozinejad Incompatible Triangular (NIT) elements. In this study, several benchmark problems are solved by using four proposed elements. These structures were previously analyzed by analytical or numerical schemes. Findings clearly indicated the improvement of answers, when various behaviors of the plate bending structures were studied. Additionally, it is concluded that the solution time is considerably declined if the recommended stress-based elements are utilized.

A locking-free formulation for three-dimensional isogeometric analysis

Non-uniform rational B-splines (NURBS)-based isogeometric analysis (IGA) suffers from locking while analyzing highly slender geometries or problems dominated by incompressibility or near incompressibility constraint. The authors have recently proposed a class of reliable and efficient NURBS-based hybrid elements to alleviate locking in two-dimensional linear elasticity regime. Nevertheless, in several practical situations, the problem often necessitates the three-dimensional elements to analyze an accurate behavior of the domain. In the present work, novel stress-based elements are introduced to eliminate the adverse effects of locking in three-dimensional linear elastic NURBS-based IGA. The comprehensive assessment of several benchmark numerical examples shows the method’s capabilities.

Collapse analysis of soils by adaptive pseudo-static limit analysis

The prediction of failure load factor and stress distribution at limit state plays an important role in geo-technical engineering design. This paper develops a pseudo-lower bound numerical procedure for adaptive limit analysis of geo-mechanics problems governed by the Mohr–Coulomb failure criterion. Equilibrium equations for the residual stress are enforced in a weak manner, allowing the use of displacement-based elements within the static limit analysis framework. The method does not require the construction of stress-based elements, but the stress fields at limit state can still be obtained. Non-linear failure criterion is cast in the form of a standard conic constraint, enabling the use of the highly efficient second-order cone based solvers. A refinement indicator based on Mohr–Coulomb yield function values is proposed, and adaptive mesh refinement is performed to speed up the computational progress. The proposed method is applied to various soil engineering problems, providing accurate bearing capacity together with stress distribution at limit state.

Strength-based topology optimisation of plastic isotropic von Mises materials

Conventionally, topology optimisation is formulated as a non-linear optimisation problem, where the material is distributed in a manner which maximises the stiffness of the structure. Due to the nature of non-linear, non-convex optimisation problems, a multitude of local optima will exist and the solution will depend on the starting point. Moreover, while stress is an essential consideration in topology optimisation, accounting for the stress locally requires a large number of constraints to be considered in the optimisation problem; therefore, global methods are often deployed to alleviate this with less control of the stress field as a consequence. In the present work, a strength-based formulation with stress-based elements is introduced for plastic isotropic von Mises materials. The formulation results in a convex optimisation problem which ensures that any local optimum is the global optimum, and the problems can be solved efficiently using interior point methods. Four plane stress elements are introduced and several examples illustrate the strength of the convex stress-based formulation including mesh independence, rapid convergence and near-linear time complexity.

Limit state analysis of reinforced concrete plates subjected to in-plane forces

A finite element formulation of rigid-plastic plates subjected to in-plane forces is developed using stress-based elements and linear programming. Three elements are established, namely a triangular plate element, a bar element and a beam element. The problem is formulated as a lower bound solution, and the dual variables are interpreted as displacements. Both load and material optimization are formulated. The method is applied to concrete plate structures modeling both the distributed and the concentrated reinforcement. An efficient computational scheme is used, thereby reducing the size of the problem. Finally, numerical examples are presented to show the capabilities of the method.

LimitS—A system for limit state analysis and optimal material layout

A system Limits for limit state analysis and material optimization has been developed and implemented in a PC environment. The program is formulated in a general finite element format with stress-based elements. The solution method is based on the lower-bound theorem, where an optimal stress distribution or an optimal material layout is determined. Through linearization of the yield criteria the optimization problem is stated as a linear programming problem. Within the formulation of the discretized model the optimal lower-bound solution is shown to be an upper-bound solution, and thereby both the statics and kinematics of the collapse mode are determined via the dual variables of the LP-problem. In Limits the following element types are implemented: two- and three-dimensional beam elements; truss elements; triangular slab elements; and shear and stringer elements for plates with in-plane loading. Examples of all three problem types are given including both limit state analysis and material optimization.

An efficient implementation of limit state calculations based on lower-bound solutions

Limit state problems are formulated in a general finite element format with stress-based elements. The analysis method is based on the lower-bound theorem which states that stress fields in equilibrium not violating the yield criteria are possible solutions. The solution method is to find the optimal stress distribution which maximizes the load. Linearization of the yield criteria leads to a linear programming problem. In order to have an efficient implementation we have made two improvements compared to previous studies. The first implies that the number of stress parameters are reduced a priori via the equilibrium equations, and the second concerns the linear programming problem, where the traditional non-negative parameter requirement is avoided. The method is described via the plane frame problem but has also been implemented for plates.