Plane Stress Structures Research Articles

Mass minimization using the reaction-diffusion level set method by considering local stress constraints in an integral form

Research in topology optimization with stress constraints has shown that defining the stress constraint locally yields better performance compared to global methods. However, an examination of the formulas for local stress constraints reveals a limitation - the constraint is only satisfied at points where it is explicitly defined, failing to guarantee satisfaction across the entire design domain. To address this shortcoming, this paper proposes utilizing an integral form of the stress constraint. The integral formulation theoretically ensures that the stress constraint is satisfied over whole design domain. The objective is to minimize the mass of plane stress structures using reaction-diffusion level set method while incorporating local stress constraints in this integral form. The methodology utilizes finite element approximations for geometry and displacements, defining local stress constraints through an integral formulation. A Lagrangian function combines objective and constraint functions, with sensitivity analysis performed during optimization based on level set function changes. Structural boundaries are updated using the Hamilton-Jacobi equation. The paper presents numerical examples with varying loads and support conditions to demonstrate the effectiveness of this integral stress constraint approach. Results illustrate the capability of the proposed method to generate optimal topologies while satisfying stress constraints across the entire design space.

Free vibration analysis employing strain gradient notation four-node plane elements and considering the effects of parasitic shear

In this work, plane stress free vibration is performed using four-node elements formulated using strain gradient notation. Accurate results are sought, and the effects of parasitic shear are investigated. By applying strain gradient notation, which is a physically interpretable notation, parasitic shear terms are identified a priori in the shear strain expressions of the four-node plane element. Parasitic shear is the source of shear locking in that element, and the a priori removal of the parasitic shear terms corrects the element for locking. Several studies in the literature show that this modeling error causes improper behavior of the element in bending, which affects the computed results of stress and displacements of the structure. Based on this, this work applies strain gradient notation to examine the effects of parasitic shear on the natural frequencies and corresponding mode shapes of plane stress structures. The results are compared with literature results, and with the isoparametric FEM formulation modeled by ANSYS software. It is observed that parasitic shear has a higher preponderance in coarse meshes of flexural vibration modes. Furthermore, the deleterious effects are emphasized as bending deformation becomes more important in the model. Strain gradient notation shows advantages in the numerical aspect and successfully eliminates the parasitic shear terms from the four-node element. The problems studied here display accurate results.

Structural optimization considering smallest magnitude eigenvalues: a smooth approximation

An issue that frequently arises in structural optimization problems considering eigenvalues is the non differentiability of repeated eigenvalues. In order to overcome this difficulty, several schemes were already presented in the literature. However, these approaches generally have other disadvantages such as the inclusion of additional constraints, the inaccuracy of representation of smallest/largest eigenvalues, the significant increase in the computational effort required and incompatibility with finite differences schemes. In this paper a smooth p-norm approximation for the smallest magnitude eigenvalue is employed. The resulting approximation is differentiable, converges to the exact value as p is increased and is very simple to use (it is also compatible with finite difference schemes). Although the use of smooth approximations for maximum/minimum operators is a classical approach, for some reason it was not extensively studied in the context of structural optimization considering eigenvalues. Three examples concerning topology optimization for the maximization of the first natural vibration frequency of plane stress structures are presented in order to show the effectiveness of the proposed approach.

Methodology for in situ stress intensity factor determination on cracked structures by digital image correlation

PurposeThe purpose of this paper is to develop a methodology for in situ stress intensity factor (SIF) determination that can be used for the analysis of cracked structures. The technique is based on digital image correlation (DIC) combined with an overdetermined algorithm.Design/methodology/approachThe linear overdeterministic algorithm for calculating the SIF based on stress values around the crack tip is applied to a strain field obtained by DIC.FindingsAs long as the image quality is sufficiently high, a good accuracy can be obtained for the measured SIF. The crack tip can be automatically detected based on the same strain field. The use of the strain field instead of the displacement field, eliminates problems related to the rigid body motion of the analysed structure.Practical implicationsIn future works, based on the applied techniques, the SIF of complex cracked plane stress structures can be accurately determined in real engineering applications.Originality/valueThe paper demonstrates application of known techniques, refined for other applications, also the use of stress field for SIF overdeterministic calculations.

Evolutionary Structural Topology Optimization for Continuum Structures with Structural Size and Topology Variables

In this paper, a topology optimization method mixed structures with continuum and discrete elements is proposed. First, based on the stress and displacement formulations of the finite element analysis, a set of stress sensitivity numbers for beam and plane-stress structures are derived. Then, relative difference quotients for topology and size variables of mixed continuum structures with several different types of components are formulated. The optimization criteria, which incorporate the element stress level and relative different quotients, are developed for the topology optimization of continuum domains and the sizing optimization of discrete elements. A new optimization procedure based on the bi-directional evolutionary structural optimization method is proposed. Two examples are provided to demonstrate the validity and effectiveness of the proposed method.

A performance-based optimization method for topology design of continuum structures with mean compliance constraints

A performance-based optimization (PBO) method for optimal topology design of linear elastic continuum structures with mean compliance constraints is presented in this paper. The performance-based design concept is incorporated in continuum topology optimization, which is treated as the problem of improving the performance of a continuum design domain in terms of the efficiency of material usage and overall stiffness. A simple scheme is employed in the proposed method to suppress the formation of checkerboard patterns. Two energy-based performance indices are derived for quantifying the topology performance of plane stress structures and plates in bending. Performance-based optimality criteria incorporating performance indices are proposed, and can be used in any continuum topology optimization methods for compliance minimization problems to obtain the optimum. Numerical examples are provided to demonstrate the effectiveness and validity of the PBO method in producing optimal topologies of continuum structures.

Optimality criteria-based algorithms for plane-stress elastoplastic structures

Optimization problems for plane-stress structures made of work-hardening elasto-plastic materials are theoretically considered. The deformation theory of plasticity is used. Optimality conditions for mean structural compliance minimization problems are obtained and investigated, and it is shown that the conditions lead to fully-stressed design. On the basis of the theoretical results obtained several optimization algorithms for the structures are developed. Numerical test results for the alogrithms are presented and analysed. High convergence rates of the algorithms are demonstrated. Significant physical properties of the numerical results are discussed.

Decomposition in optimal plastic design of structures

A structural synthesis procedure based on the Dantzig-Wolfe decomposition principle is developed for the optimal plastic design of structures subject to multiple load conditions. The decomposed structural synthesis problems consist of a restricted master and a number of subproblems. Each subproblem is further divided into second-level subproblems for which closed form solutions are obtained. The decomposition procedure generates not only an optimal solution for the plastic design problem but also the collapse mechanism associated with the optimal design. An optimal solution generated by the decomposition procedure is shown to be a saddle point for the associated Lagrangian function, which is sufficient for global optimally and zero duality gap. The dual problem for the optimal plastic structural design is interpreted as the maximization of the total power of loads, subject to limitations on the total specific power of dissipation in each structural member. Numerical results for a collection of two- and three-dimensional structures are generated by the decomposition procedure. The computational efficiency and numerical accuracy are confirmed by comparison with previously reported results for trusses and approximate solutions for plane stress structures.

Direct prediction of fracture for two-dimensional plane stress structures

This paper presents a procedure for the direct prediction of fracture in two-dimensional structures subjected to plane stress conditions as the result of monotonically increasing loads. The procedure is based on standard finite element methods coupled with incrementally linear element material properties and a zero modulus-unload reload scheme to advance the fracture surface. Comparisons of numerical and experimental data show that the procedure can accurately predict load-deflection curves, load and deflection at fracture, and fracture initiation sites for two-dimensional structures with either mild or severe stress concentrations located anywhere in the structure. Plasticity zones and stable or unstable fracture can also be predicted. The procedure is shown to highly dependent on the mesh density along anticipated crack paths for severe stress concentrations.