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Current research in the field of limit analysis is focussing on the development of\ud numerical tools which are sufficiently efficient and robust to be used in engineering\ud practice. This places demands on the numerical discretisation strategy adopted\ud as well as on the mathematical programming tools applied, which are the key\ud ingredients of a typical computational limit analysis procedure. In this research,\ud the Element-Free Galerkin (EFG) discretisation strategy is used to approximate\ud the displacement and moment fields in plate and slab problems, and second-order\ud cone programming (SOCP) is used to solve the resulting discretised formulations.\ud A numerical procedure using the EFG method and second-order cone programming\ud for the kinematic limit analysis problem was developed first. The moving\ud least squares technique was used in combination with a stabilised conforming nodal\ud integration scheme, both to keep the size of the optimisation problem small and to\ud provide stable and accurate solutions. The formulation was expressed as a problem\ud of minimizing a sum of Euclidean norms, which was then transformed into a\ud form suitable for solution using SOCP.\ud To improve the accuracy of solutions and to speed-up the computational process,\ud an efficient h-adaptive EFG scheme was also developed. The naturally conforming\ud property of meshfree approximations (with no nodal connectivity required) facilitates\ud the implementation of h-adaptivity. The error in the computed displacement\ud field was estimated accurately using the Taylor expansion technique. A stabilised\ud conforming nodal integration scheme was also extended to error estimators, leading\ud to an efficient and truly meshfree adaptive method.\ud To obtain an indication of bounds on the solutions obtained, an equilibrium formulation\ud was also developed. Pure moment fields were approximated using a\ud moving least squares technique. The collocation method was used to enforce the\ud strong form of the equilibrium equations and a stabilised conforming nodal integration\ud scheme was introduced to eliminate numerical instability problems. The von\ud Mises and Nielsen yield criteria were then enforced by introducing second-order\ud cone constraints

Publisher: Civil and Structural Engineering (Sheffield)

Year: 2010

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- 2006b Upper bound limit analysis using simplex strain elements and second-order cone programming.
- (2000). A 2-D meshless model for jointed rock structures.
- (1983). A boundary element approach to limit analysis,
- (1990). A class of mixed assumed strain methods and the method of incompatible modes.
- (1998). A computerised method for rigid-plastic yield-line analysis of slabs.
- (1997). A ﬁnite element formulation of the rigid-plastic limit analysis problem.
- (1999). A ﬁnite element method for crack growth without remeshing.
- (1973). A ﬁnite element, linear programming methods for the limit analysis of thin plates.
- (2003). A general nonlinear optimization algorithm for lower bound limit analysis. International Journal for Numerical Methods in Engineering 56, 165–184.Chapter 8. Conclusions and future work 169
- (2001). A meshless method for Kirchhoﬀ plate bending problems.
- (1992). A method of estimating limit loads by iterative elastic analysis. I – Simple examples.
- (1999). A mixed ﬁnite element model for plane strain limit analysis computations.
- (1982). A mixed formulation and mixed ﬁnite elements for limit analysis.
- (1998). A modiﬁed collocation method and a penalty formulation for enforcing the essential boundary conditions in the element free Galerkin method.
- (1994). A new implementation of the ElementFree Galerkin method.
- (2007). A non-linear programming method approach for upper bound limit analysis.
- (1977). A numerical approach to testing the ﬁssion hypothesis.
- (1995). A numerical method for plastic limit analysis of 3-D structures.
- (1994). A quadratic element for upper bound limit analysis.
- (1968). A quadratic programming approach for certain classes of non linear structural problems. Meccanica 1, 121–130.Chapter 8. Conclusions and future work 173
- (1987). A simple error estimator and adaptive procedure for practical engineering analysis.
- (2006). A simple error indicator for meshfree methods based on natural neighbors.
- (2007). A smoothed ﬁnite element method for mechanics problems.
- (2001). A stabilized conforming nodal integration for Galerkin mesh-free methods.
- (1999). Adaptive analysis of yield line patterns in plates with the arbitrary Lagrangian-Eulerian method.
- (2003). Adaptive F.E. method for the shakedown and limit analysis of pressure vessels.
- (2005). Adaptivity for structured meshfree particle methods in 2D and 3D.
- (2000). Advanced spatial discretisation strategies for localised failure: mesh adaptivity and meshless methods,
- (1996). Advances in multiple scale kernel particle methods. Computational Mechanics 18, 73–111.Chapter 8. Conclusions and future work 171
- (2001). An adaptive approach to limit analysis.
- (1998). An adaptive approach with the ElementFree-Galerkin method.
- (2002). An adaptive procedure based on background cells for meshless methods.
- (1996). An eﬃcient Newton barrier method for minimizing a sum of Euclidean norms.
- (2005). An Introduction to Meshfree Methods and Their Programming.
- (1988). An introduction to SPH.
- (1993). An iterative algorithm for limit analysis with nonlinear yield functions.
- (2006). Analysis of plates and laminates using the element-free Galerkin method.
- (1995). Analysis of thin plates by the Element-Free Galerkin method.
- (1996). Analysis of thin shells by the element-free Galerkin method.
- (2007). Application of Discontinuity Layout Optimization to Plane Plasticity Problems.
- (2000). Application of essential boundary conditions in mesh-free methods: a corrected collocation method.
- (1998). Applications of secondorder cone programming. Linear Algebra and its Applications
- (1995). Atlas of limit loads of metal plates, shells and disks. Elsevier.Chapter 8. Conclusions and future work 176
- (2001). Automatic mesh reﬁnement in limit analysis.
- (2004). Boundary element methods for lower bound limit and shakedown analysis.
- (1967). Calcul plastique des constructions. Centre BelgoLuxembourgeois d’Information de L’Acler.Chapter 8. Conclusions and future work 174
- (1982). Calculation of collapse loads using higher order elements. in:
- (1984). CEPAO-an automatic program for rigid-plastic and elasticplastic analysis and optimization of frame structures. Engineering Structures 6, 35–51.Chapter 8. Conclusions and future work 175
- (2003). Classiﬁcation and overview of meshfree methods.
- (1981). Computation of limit load.
- (1991). Computation of the collapse state in limit analysis using the LP aﬃne scaling algorithm.
- (2008). Computational Geometry: Algorithms and Applications.
- (1998). Computing limit loads by minimizing a sum of norms.
- (1999). Conclusions and future work 161 Askes,
- (1997). Consistent pseudo-derivatives in meshless methods.
- (2008). Convergence and stabilization of stress-point integration in mesh-free and particle methods.
- (2000). Correction and stabilization of smooth particle hydrodynamics methods with applications in metal forming simulations.
- (1976). Direct limit analysis via rigid-plastic ﬁnite elements.
- (2001). Displacement and equilibrium models in the ﬁnite element method.
- (2002). Dual analysis by a meshless method.
- (1996). Dynamic fracture using Element-Free Galerkin methods.
- (1999). Elastic crack growth in ﬁnite elements with minimal remeshing.
- (1967). Elasto-plastic analysis of two-dimensional stress systems by the element method.
- (1967). Elasto-plastic matrix displacement analysis of threedimensional stress systems by ﬁnite element method.
- (2000). Element-free Galerkin methods for dynamic fracture in concrete.
- (1996). Element-free Galerkin methods for static and dynamic fracture.
- (1979). Engineering plasticity by mathematical programming.
- (2000). Enrichment and coupling of the ﬁnite element and meshless methods.
- (1978). Error estimates for adaptive ﬁnite element computations.
- (2006). Error estimation and adaptive discretisation for quasi-brittle failure,
- (1998). Explicit reproducing kernel particle methods for large deformation problems.
- (1952). Extended limit design theorems for continuous medium.
- (2006). Extension of the linear matching method to geotechnical problems.
- (2003). Filters, reproducing kernel, and adaptive meshfree method.
- (1976). Finite element analysis assuming rigid-ideal-plastic material behaviour. Limit analysis using ﬁnite elements,
- (1972). Finite element limit analysis using linear programming.
- (1980). Finite element method and limit analysis theory for soil mechanics problems.
- (1974). Finite element techniques in plane limit problems.
- (2007). Formulation and solution of some plasticity problems as conic programs.
- (1980). Generalization of selective integration procedures to anisotropic and nonlinear media.
- (1992). Generalizing the ﬁnite element method: diﬀuse approximation and diﬀuse elements.
- (2009). Gradient and dilatational stabilizations for stresspoint integration in the element-free Galerkin method. International Journal for Numerical Methods in Engineering 77, 776–798.Chapter 8. Conclusions and future work 166
- (2002). Inelastic analysis of structures.
- (2001). Lagrangian meshfree formulation for analysis of geotechnical materials.
- (1997). Large deformation analysis of rubber based on a reproducing kernel particle method.
- (2001). Lectures on Modern Convex Optimization: Analysis, Algorithms, and Engineering Applications. Society for Industrial Mathematics.
- (1998). Limit analysis and concrete plasticity.
- (1994). Limit analysis and optimal design of plates with equilibrium elements.
- (2000). Limit analysis for a general class of yield conditions.
- (1974). Limit analysis for plates: The exact solution for a clamped square plate of isotropic homogeneous material obeying the square yield criterion and loaded by uniform pressure.
- (1980). Limit analysis in plasticity as a mathematical programming problem.
- (1994). Limit analysis of anisotropic soils using ﬁnite elements and linear programming.
- (1996). Limit analysis of collapse states. Handbook of Numerical Analysis, Elsevier Science
- (1970). Limit analysis of plane problems in soil mechanics.
- (1999). Limit analysis of plates -a ﬁnite element formulation.
- (2009). Limit analysis of plates using the EFG method and second-order cone programming.
- (1972). Limit analysis of plates with piecewise linear yield surface.
- (1964). Limit analysis of reinforced concrete slabs.
- (1963). Limit analysis of rotationally symmetric plates and shells.
- (1967). Limit analysis of rotationally symmetric shells under central boss loading by a numerical method.
- (1996). Limit analysis of solids and structures.
- (1995). Limit analysis with the dual aﬃne scaling algorithm.
- (1972). Limit analysis: The development of a concept.
- (1968). Limit load of a cantilever in plane stress. In: Engineering plasticity edited by
- (2005). Limit loads for multilayered half-space using the linear matching method.
- (1997). Limit state solutions, based upon linear elastic solutions with a spatially varying elastic modulus.
- (2007). Limit theorems for gradient-dependent elastoplastic geomaterials.
- (1954). Load-carrying capacities for circular plates of perfectly-plastic material with arbitrary yield condition.
- (2004). Locking-free stabilized conforming nodal integration for meshfree Mindlin-Reissner plate formulation.
- (2006). Lower bound limit analysis of cohesive-frictional materials using second-order cone programming.
- (2002). Lower bound limit analysis of slabs with nonlinear yield criteria.
- (1988). Lower bound limit analysis using ﬁnite elements and linear programming.
- (2002). Lower bound limit analysis using nonlinear programming.
- (2005). Lower bound limit analysis with adaptive remeshing.
- (2008). Lower-bound limit analysis by using the EFG method and non-linear programming.
- (1977). Mathematical programming methods for deformation analysis at plastic collapse.
- (1950). Mathematical theory of plasticity.
- (2008). Mesh adaptive computation of upper and lower bounds in limit analysis.
- (2003). Mesh Free Methods: Moving Beyond the Finite Element Method.
- (2003). Mesh generation for lower bound limit analysis.
- (2002). Meshfree and particle methods and their applications.
- (2004). Meshfree methods.
- (1998). Meshless methods for shear-deformable beams and plates.
- (2006). Meshless Methods in Solid Mechanics.
- (1996). Meshless methods: An overview and recent developments.
- (1997). Moving least-square reproducing kernel methods (I) methodology and convergence.
- (1997). Multi-resolution reproducing kernel particle method for computational ﬂuid dynamics.
- (1999). Multiple scale meshfree methods for damage fracture and localization.
- (1998). Multiple-scale reproducing kernel particle methods for large deformation problems.
- (2005). Negative penalty functions in the elementfree Galerkin method.
- (2000). New concepts in meshless methods.
- (2007). Nonlinear analysis of plates and laminates using the element free Galerkin method.
- (2004). Numerical determination of limit loads for three-dimensional structures using boundary element method.
- (1968). Numerical Methods for the Limit Analysis of Plates.
- (1982). Numerical prediction of collapse loads using ﬁnite element methods.
- (2000). Numerical simulations of large deformation of thin shell structures using meshfree methods. Computational Mechanics 25, 102–116.Chapter 8. Conclusions and future work 170
- (2000). Numerical simulations of strain localization in inelastic solids using mesh-free methods.
- (2003). On implementing a primal-dual interior-point method for conic quadratic programming.
- (1965). On linear programming and plastic limit analysis.
- (1974). On numerically accurate ﬁ-nite element solutions in the fully plastic range.
- (1998). On the completeness of meshfree particle methods.
- (2001). On the safety of the strip method for reinforced concrete slab design.
- (1947). On variational principles in theory of plasticity.
- (2003). Performance of the p-version ﬁnite element method for limit analysis.
- (1997). Plastic analysis and design of plates, shells and disks. North-Holland publishing company - second edition.
- (1959). Plastic analysis of structures. Robert E. Krieger Publishing Co.
- (1961). Plastic and elastic design of slabs and plates. London: Thames and Hudson.
- (1988). Plasticity for structural engineers.
- (1990). Plasticity theory.
- (1975). Plasticity.
- (1971). Reduced integration technique in general analysis of plates and shells.
- (2000). Regularization of material instabilities by meshfree approximations with intrinsic length scales.
- (2009). Remarks on some properties of conic yield restrictions in limit analysis.
- (1999). Reproducing kernel hierarchical partition of unity part ii:
- (1995). Reproducing kernel particle methods.
- (2001). Shakedown and limit analyses for 3-D structures using the linear matching method.
- (1992). Shakedown and limit analysis by the boundary integral equation method.
- (2008). Smooth ﬁnite element methods: Convergence, accuracy and properties.
- (1977). Smooth particle hydrodynamics: theory and applications to non spherical stars.
- (2004). Stabilized conforming nodal integration in the natural-element method.
- (2004). Stabilized conforming nodal integration: exactness and variational justiﬁcation.
- (1967). Strain-energy bounds in ﬁnite element analysis by slab analogy.
- (1981). Surfaces generated by moving least squares methods.
- (1972). The collapse load of reinforeced concrete plates.
- (2000). The Finite Element Method, Volume 1: The Basis. Butterworth-Heinemann; 5 edition.
- (1961). The Mises yield condition for ratationally symmetric shells.
- (2008). The MOSEK optimization toolbox for MATLAB manual. http://www.mosek.com, version 5.0 edn, Mosek ApS.
- (1999). The relationship of some a posteriori estimators.
- (1992). The superconvergent patch recovery (SPR) and adaptive ﬁnite element reﬁnement.
- (2007). Theoretical aspects of the smoothed ﬁnite element method (SFEM).
- (1988). Theory of plasticity.
- (1964). Traglast und optimale Bemessung von Platten.
- (2007). Two and three dimensional bearing capacity of footings in sand.
- (2009). Upper and lower bounds in limit analysis: Adaptive meshing strategies and discontinuous loading.
- (2008). Upper bound limit analysis using discontinuous quadratic displacement ﬁelds.
- (1995). Upper bound limit analysis using discontinuous velocity ﬁelds.
- (1989). Upper bound limit analysis using ﬁnite elements and linear programming.
- (2002). Upper bound limit analysis using linear ﬁnite elements and non-linear programming.
- (1999). Volumetric locking in the Element-Free Galerkin method.
- (1995). Wavelet and multiple scale reproducing kernel methods.
- (1978). Yield line method by ﬁnite elements and linear programming.
- (1995). Yield-line analysis by sequential linear programming.
- (1962). Yield-line theory. London: Cement and Concrete Association.

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