Francis Tin-loi | The University of New South Wales (original) (raw)

Papers by Francis Tin-loi

Research paper thumbnail of An MPEC approach for the critical post-collapse behavior of rigid-plastic structures

International Journal of Solids and Structures, 2011

This paper presents a numerical method to identify and trace the critical post-collapse response ... more This paper presents a numerical method to identify and trace the critical post-collapse response of rigid perfectly-plastic structures. To account for the possibility of multiple equilibrium paths, the critical one is directly identified using the minimum 2nd-order work criterion. Our proposed enhanced sequential limit analysis is formulated as an instance of the challenging class of optimization problems known as a mathematical program with equilibrium constraints (MPEC). This MPEC formulation minimizes the 2nd-order work expression subject to the set of constraints describing the complete complementarity system (in mixed static-kinematic variables) governing simultaneously the two adjacent equilibrium configurations, namely the current one and its neighboring state. We use a nonlinear programming based algorithm, involving relaxation of the complementarity terms, to solve the MPEC. Four numerical examples are provided to illustrate application of the proposed scheme.

Research paper thumbnail of Mathematical programming approaches for the safety assessment of semirigid elastoplastic frames

International Journal of Solids and Structures, 2011

This paper presents two complementary mathematical programming based approaches for the accurate ... more This paper presents two complementary mathematical programming based approaches for the accurate safety assessment of semirigid elastoplastic frames under quasistatic loads. The inelastic behavior of the flexible connections and material plasticity are accommodated through piecewise linearized nonlinear yield surfaces. As is necessary for this class of structures, geometric nonlinearity is taken into account. Moreover, only a 2nd-order geometric approximation is included as this is sufficiently accurate for practical structures. The work described has a twofold contribution. First, we develop an algorithm that can robustly and efficiently process the complete (path-dependent) nonholonomic response of the structure in a stepwise (path-independent) holonomic fashion. The governing formulation is cast in mixed statickinematic variables and leads naturally to what is known in the mathematical programming literature as a mixed complementarity problem (MCP). The novelty of the proposed algorithm is that it processes the MCP directly without using some iterative (and often cumbersome) predictor-corrector procedure. Second, in the spirit of simplified analyses, the classical limit analysis approach is extended to compute the limit load multiplier under the simultaneous influence of joint flexibility, material and geometric nonlinearities, and limited ductility. Our formulation is an instance of the challenging class of optimization problems known as a mathematical program with equilibrium constraints (MPEC). Various nonlinear programming based algorithms are proposed to solve the MPEC. Finally, four numerical examples, concerning practical structures and benchmark cases, are provided to illustrate application of the analyses as well as to validate the accuracy and robustness of the proposed schemes.

Research paper thumbnail of On the numerical solution of a class of unilateral contact structural optimization problems

Structural Optimization, 1999

This paper deals with a special class of structural optimization problems in nonsmooth mechanics.... more This paper deals with a special class of structural optimization problems in nonsmooth mechanics. More precisely, it is required to minimize the weight of a structure subject to frictionless unilateral contact conditions and constraints on the magnitudes of contact forces, displacements, stresses and cross-sectional areas. This problem, as is well-known, can be formulated as a special and challenging optimization problem known as a Mathematical Program with Equilibrium Constraints (MPEC), a key feature of which is the presence of complementarity conditions, involving the orthogonality of two sign-constrained vectors. In spite of its inherent nonsmoothness, we attempt to solve the problem using standard nonlinear programming techniques. In particular, we investigate numerically the application of two simple algorithms, both based on the use of the general-purpose nonlinear programming code CONOPT accessed via the powerful GAMS modelling language, for solving the suitably reformulated problem. Application is illustrated by means of three numerical examples.

Research paper thumbnail of Optimum shakedown design under residual displacement constraints

Structural and Multidisciplinary Optimization, 2000

We consider the minimum weight design of suitably discretized elastoplastic structures subjected ... more We consider the minimum weight design of suitably discretized elastoplastic structures subjected to variable repeated loads and constraints on the amount of residual (or permanent) deflections. The optimization problem is formulated on the basis of the classical lower bound theorem of shakedown, supplemented by appropriate constraints on deflections obtained from existing bounding results. The primary purpose of the paper is to show that, even for large size structures, this important and challenging problem can be modeled and solved directly as a mathematical programming problem within the industry standard modeling framework GAMS. Examples concerning truss-like structures are presented for illustrative purposes.

Research paper thumbnail of An entropic optimization approach for a parameter identification problem in quasibrittle fracture

Structural and Multidisciplinary Optimization, 2004

ABSTRACT

Research paper thumbnail of Shakedown of Frames with Semirigid Connections

Journal of Structural Engineering, 1993

ABSTRACT

Research paper thumbnail of Post‐Yield Analysis of Rigid‐Plastic Beams with Variable Restraints

Journal of Engineering Mechanics, 1991

ABSTRACT

Research paper thumbnail of Analysis and plastic synthesis of frames involving frictional contacts

IOP Conference Series: Materials Science and Engineering, 2010

This paper presents novel schemes for the extended limit analysis and plastic synthesis of rigid ... more This paper presents novel schemes for the extended limit analysis and plastic synthesis of rigid perfectly plastic frames involving unilateral supports with frictional contacts. The focus is on the Coulomb friction model which embodies a nonassociative complementarity condition. As such, uniqueness of the upper bound solution in the complementarity system is no longer guaranteed. The aim of the extended limit analysis is to compute, for fixed topology and known material distribution, the least upper bound to collapse limit. This is achieved by directly formulating and solving a single nonconvex and nonsmooth optimization problem, known in a literature as a mathematical program with equilibrium constraints (MPEC). Under given design loads, the plastic synthesis can also be carried out using an iterative scheme that determines the safe material distribution such that the total weight of the structure is a minimum.

Research paper thumbnail of Reply to discusser's comments: Tin-Loi F, Ngo NS. Performance of the -version finite element method for limit analysis. International Journal of Mechanical Sciences (2003); 45(6–7): 1149–66

International Journal of Mechanical Sciences, 2005

Research paper thumbnail of Limit analysis of elastoplastic frames considering 2nd-order geometric nonlinearity and displacement constraints

International Journal of Mechanical Sciences, 2009

The present paper extends the classical limit analysis of plane frames to account for 2nd-order g... more The present paper extends the classical limit analysis of plane frames to account for 2nd-order geometric nonlinearity. Any specified displacement limits can also be included in the proposed analysis. The effect of combined bending moment and axial force is accommodated in the adopted piecewise linearized yield condition, albeit still assumed as perfectly plastic. The main feature of the novel approach proposed is to compute simultaneously, in a single step, the maximum load and corresponding deformations of the structure under limited displacement conditions. The problem is cast as an instance of the challenging class of (nonconvex and nonsmooth) mathematical programs with equilibrium constraints (MPECs). Various nonlinear programming based algorithms are proposed to solve the MPEC. Four numerical examples are provided to illustrate application of the proposed limit analysis approach and to highlight the necessity of considering geometric nonlinearity for a more realistic assessment of structural behavior.

Research paper thumbnail of Limit analysis of frames involving unilateral supports with frictional contact

International Journal of Mechanical Sciences, 2007

ABSTRACT We consider the classical limit analysis problem of frame structures made up of rigid pe... more ABSTRACT We consider the classical limit analysis problem of frame structures made up of rigid perfectly plastic members and involving some supports in unilateral frictional contact with the ground. A direct formulation as a mixed complementarity problem (MCP) is used. For the Coulomb case, which forms the focus of this paper, the corresponding MCP may admit multiple upper bound collapse load solutions. In order to identify the least upper bound solution, we propose two algorithms. The first one attempts to enumerate the possible multiple solutions, or at least map the solution space if the solutions are connected. The second scheme tries to find the least upper bound by directly formulating and solving a single nonconvex optimization problem, known in the literature as a mathematical program with equilibrium constraints (MPEC). Two simple examples are provided to illustrate application of these approaches. They also serve to highlight some key features of such structures.

Research paper thumbnail of Performance of the p-version finite element method for limit analysis

International Journal of Mechanical Sciences, 2003

In this paper, we investigate the use of the p-version finite element method in carrying out limi... more In this paper, we investigate the use of the p-version finite element method in carrying out limit analysis using a mathematical programming-based static approach. An important motivation for this study is to overcome the well-known locking behavior—caused by the incompressibility constraint—that may occur in plane strain and 3D problems for such common yield criteria as von Mises’. Quadrilateral elements and

Research paper thumbnail of A constrained non-linear system approach for the solution of an extended limit analysis problem

International Journal for Numerical Methods in Engineering, 2009

A number of recent papers (see, e.g. (Int. have shown that classical limit analysis can be extend... more A number of recent papers (see, e.g. (Int. have shown that classical limit analysis can be extended to incorporate such important features as geometric non-linearity, softening and various so-called ductility constraints. The generic formulation takes the form of a challenging (nonconvex and nonsmooth) optimization problem referred to in the mathematical programming literature as a mathematical program with equilibrium constraints (MPEC). Similar to a classical limit analysis, the aim is to compute in a single step a bound (upper bound, in the case of the extended problem) to the maximum load. The solution algorithm so far proposed to solve the MPEC is to convert it into an iterative non-linear programming problem and attempts to process this using a standard non-linear optimizer. Motivated by the fact that no method is guaranteed to solve such MPECs and by the need to avoid the use of an optimization approach, which is unfamiliar to most practising engineers, we propose, in the present paper, a novel numerical scheme to solve the MPEC as a constrained non-linear system of equations. We illustrate the application of this approach using the simple class of elastoplastic softening skeletal structures for which certain ductility conditions are prescribed.

Research paper thumbnail of Simultaneous ultimate load and deformation analysis of strain softening frames under combined stresses

Engineering Structures, 2008

This paper presents a method for carrying out, in a single step, an elastoplastic analysis to obt... more This paper presents a method for carrying out, in a single step, an elastoplastic analysis to obtain simultaneously both the ultimate load and corresponding deformation of a strain softening structure. The effect of combined bending moment and axial force is also accounted for in the piecewise linearized softening yield condition. However, a monotonic loading process is assumed within a small displacement framework. We propose a mathematical programming approach to tackle this problem. In particular, the formulation leads to an instance of the challenging class of a so-called "mathematical program with equilibrium constraints" (MPEC). Various nonlinear programming based algorithms are proposed to solve the MPEC. Numerical examples are provided to illustrate the described analysis and also to highlight the effects of constitutive local softening instability and of axial forces on the overall structural behavior of the frames.

Research paper thumbnail of Collapse load evaluation of structures with frictional contact supports under combined stresses

Computers & Structures, 2011

ABSTRACT This paper extends classical limit analysis to structures for which some supports are su... more ABSTRACT This paper extends classical limit analysis to structures for which some supports are subjected to “nonstandard” unilateral frictional contact with the ground. A typical and commonly adopted model is nonassociative Coulomb friction. For such cases, the use of the classical bound theorems is not possible. Moreover, simply solving the governing equations as a mixed complementarity problem (MCP) does not guarantee that the best bound has been calculated. We have therefore developed an approach that attempts to compute, in a single step, the critical (least) upper bound solution by formulating and solving an instance of the challenging class of optimization problems, known as a mathematical program with equilibrium constraints (MPEC). Two examples are provided to illustrate application of the proposed scheme, as well as to highlight some key features of such structures.

Research paper thumbnail of Modeling Fracture in Masonry

Journal of Structural Engineering, 2007

A finite element procedure developed for the study of fracture in concrete is extended for the si... more A finite element procedure developed for the study of fracture in concrete is extended for the simulation of tensile and/or shear fracture in masonry. Triangular units are grouped into rectangular zones mimicking brick units with surrounding mortar joints. Fracture is captured through a constitutive softening-fracture law at the boundary interface nodes. The mortar joint, which is a plane of weakness, can be modeled as an interface of zero thickness or of a given thickness. At each nodal location, there exist essentially two nodes, the relative ...

Research paper thumbnail of Nonlinear analysis and buckling of elastically supported circular shallow arches

International Journal of Solids and Structures, 2007

Arches are often supported elastically by other structural members. This paper investigates the i... more Arches are often supported elastically by other structural members. This paper investigates the in-plane nonlinear elastic behaviour and stability of elastically supported shallow circular arches that are subjected to a radial load uniformly distributed around the arch axis. Analytical solutions for the nonlinear behaviour and for the nonlinear buckling load are obtained for shallow arches with equal or unequal elastic supports. It is found that the flexibility of the elastic supports and the shallowness of the arch play important roles in the nonlinear structural response of the arch. The limiting shallownesses that distinguish between the buckling modes are obtained and the relationship of the limiting shallowness with the flexibility of the elastic supports is established, and the critical flexibility of the elastic radial supports is derived. An arch with equal elastic radial supports whose flexibility is larger than the critical value becomes an elastically supported beam curved in elevation, while an arch with one rigid and one elastic radial support whose flexibility is larger than the critical value still behaves as an arch when its shallowness is higher than a limiting shallowness. Comparisons with finite element results demonstrate that the analytical solutions and the values of the critical flexibility of the elastic supports and the limiting shallowness of the arch are valid.

Research paper thumbnail of Non-linear in-plane buckling of rotationally restrained shallow arches under a central concentrated load

International Journal of Non-Linear Mechanics, 2008

Research paper thumbnail of Probabilistic interval analysis for structures with uncertainty

Structural Safety, 2010

A hybrid probabilistic and interval method for engineering problems described by a mixture of ran... more A hybrid probabilistic and interval method for engineering problems described by a mixture of random and interval variables is presented. Random interval arithmetic for carrying out basic operations between random and interval variables is developed by extending interval arithmetic rules. The uncertainty of a random interval variable is represented by probabilistic as well as interval information. A random interval moment method is proposed to calculate the mean and variance of random interval variables. The solution strategy and associated numerical tool are developed by using perturbation theory and Taylor expansion for linear equations with random and interval variables. Engineering applications in structures with analytical or semi-analytical solutions are used to demonstrate the accuracy and effectiveness of the proposed method.

Research paper thumbnail of Optimal tilt lifting of beams as a min-max problem

Structural and Multidisciplinary Optimization, 2004

This paper considers the problem of finding the optimal pickup points for a beam that is to be ti... more This paper considers the problem of finding the optimal pickup points for a beam that is to be tilt lifted by a system of slings attached to a crane. Under the assumptions of a rigid beam and inextensible cables, this task is formulated as a min-max optimization problem. As for its numerical solution, we propose an efficient and robust algorithm involving smoothing and an appropriate discretization of the objective function. A typical numerical example is provided to illustrate the approach.

Research paper thumbnail of An MPEC approach for the critical post-collapse behavior of rigid-plastic structures

International Journal of Solids and Structures, 2011

This paper presents a numerical method to identify and trace the critical post-collapse response ... more This paper presents a numerical method to identify and trace the critical post-collapse response of rigid perfectly-plastic structures. To account for the possibility of multiple equilibrium paths, the critical one is directly identified using the minimum 2nd-order work criterion. Our proposed enhanced sequential limit analysis is formulated as an instance of the challenging class of optimization problems known as a mathematical program with equilibrium constraints (MPEC). This MPEC formulation minimizes the 2nd-order work expression subject to the set of constraints describing the complete complementarity system (in mixed static-kinematic variables) governing simultaneously the two adjacent equilibrium configurations, namely the current one and its neighboring state. We use a nonlinear programming based algorithm, involving relaxation of the complementarity terms, to solve the MPEC. Four numerical examples are provided to illustrate application of the proposed scheme.

Research paper thumbnail of Mathematical programming approaches for the safety assessment of semirigid elastoplastic frames

International Journal of Solids and Structures, 2011

This paper presents two complementary mathematical programming based approaches for the accurate ... more This paper presents two complementary mathematical programming based approaches for the accurate safety assessment of semirigid elastoplastic frames under quasistatic loads. The inelastic behavior of the flexible connections and material plasticity are accommodated through piecewise linearized nonlinear yield surfaces. As is necessary for this class of structures, geometric nonlinearity is taken into account. Moreover, only a 2nd-order geometric approximation is included as this is sufficiently accurate for practical structures. The work described has a twofold contribution. First, we develop an algorithm that can robustly and efficiently process the complete (path-dependent) nonholonomic response of the structure in a stepwise (path-independent) holonomic fashion. The governing formulation is cast in mixed statickinematic variables and leads naturally to what is known in the mathematical programming literature as a mixed complementarity problem (MCP). The novelty of the proposed algorithm is that it processes the MCP directly without using some iterative (and often cumbersome) predictor-corrector procedure. Second, in the spirit of simplified analyses, the classical limit analysis approach is extended to compute the limit load multiplier under the simultaneous influence of joint flexibility, material and geometric nonlinearities, and limited ductility. Our formulation is an instance of the challenging class of optimization problems known as a mathematical program with equilibrium constraints (MPEC). Various nonlinear programming based algorithms are proposed to solve the MPEC. Finally, four numerical examples, concerning practical structures and benchmark cases, are provided to illustrate application of the analyses as well as to validate the accuracy and robustness of the proposed schemes.

Research paper thumbnail of On the numerical solution of a class of unilateral contact structural optimization problems

Structural Optimization, 1999

This paper deals with a special class of structural optimization problems in nonsmooth mechanics.... more This paper deals with a special class of structural optimization problems in nonsmooth mechanics. More precisely, it is required to minimize the weight of a structure subject to frictionless unilateral contact conditions and constraints on the magnitudes of contact forces, displacements, stresses and cross-sectional areas. This problem, as is well-known, can be formulated as a special and challenging optimization problem known as a Mathematical Program with Equilibrium Constraints (MPEC), a key feature of which is the presence of complementarity conditions, involving the orthogonality of two sign-constrained vectors. In spite of its inherent nonsmoothness, we attempt to solve the problem using standard nonlinear programming techniques. In particular, we investigate numerically the application of two simple algorithms, both based on the use of the general-purpose nonlinear programming code CONOPT accessed via the powerful GAMS modelling language, for solving the suitably reformulated problem. Application is illustrated by means of three numerical examples.

Research paper thumbnail of Optimum shakedown design under residual displacement constraints

Structural and Multidisciplinary Optimization, 2000

We consider the minimum weight design of suitably discretized elastoplastic structures subjected ... more We consider the minimum weight design of suitably discretized elastoplastic structures subjected to variable repeated loads and constraints on the amount of residual (or permanent) deflections. The optimization problem is formulated on the basis of the classical lower bound theorem of shakedown, supplemented by appropriate constraints on deflections obtained from existing bounding results. The primary purpose of the paper is to show that, even for large size structures, this important and challenging problem can be modeled and solved directly as a mathematical programming problem within the industry standard modeling framework GAMS. Examples concerning truss-like structures are presented for illustrative purposes.

Research paper thumbnail of An entropic optimization approach for a parameter identification problem in quasibrittle fracture

Structural and Multidisciplinary Optimization, 2004

ABSTRACT

Research paper thumbnail of Shakedown of Frames with Semirigid Connections

Journal of Structural Engineering, 1993

ABSTRACT

Research paper thumbnail of Post‐Yield Analysis of Rigid‐Plastic Beams with Variable Restraints

Journal of Engineering Mechanics, 1991

ABSTRACT

Research paper thumbnail of Analysis and plastic synthesis of frames involving frictional contacts

IOP Conference Series: Materials Science and Engineering, 2010

This paper presents novel schemes for the extended limit analysis and plastic synthesis of rigid ... more This paper presents novel schemes for the extended limit analysis and plastic synthesis of rigid perfectly plastic frames involving unilateral supports with frictional contacts. The focus is on the Coulomb friction model which embodies a nonassociative complementarity condition. As such, uniqueness of the upper bound solution in the complementarity system is no longer guaranteed. The aim of the extended limit analysis is to compute, for fixed topology and known material distribution, the least upper bound to collapse limit. This is achieved by directly formulating and solving a single nonconvex and nonsmooth optimization problem, known in a literature as a mathematical program with equilibrium constraints (MPEC). Under given design loads, the plastic synthesis can also be carried out using an iterative scheme that determines the safe material distribution such that the total weight of the structure is a minimum.

Research paper thumbnail of Reply to discusser's comments: Tin-Loi F, Ngo NS. Performance of the -version finite element method for limit analysis. International Journal of Mechanical Sciences (2003); 45(6–7): 1149–66

International Journal of Mechanical Sciences, 2005

Research paper thumbnail of Limit analysis of elastoplastic frames considering 2nd-order geometric nonlinearity and displacement constraints

International Journal of Mechanical Sciences, 2009

The present paper extends the classical limit analysis of plane frames to account for 2nd-order g... more The present paper extends the classical limit analysis of plane frames to account for 2nd-order geometric nonlinearity. Any specified displacement limits can also be included in the proposed analysis. The effect of combined bending moment and axial force is accommodated in the adopted piecewise linearized yield condition, albeit still assumed as perfectly plastic. The main feature of the novel approach proposed is to compute simultaneously, in a single step, the maximum load and corresponding deformations of the structure under limited displacement conditions. The problem is cast as an instance of the challenging class of (nonconvex and nonsmooth) mathematical programs with equilibrium constraints (MPECs). Various nonlinear programming based algorithms are proposed to solve the MPEC. Four numerical examples are provided to illustrate application of the proposed limit analysis approach and to highlight the necessity of considering geometric nonlinearity for a more realistic assessment of structural behavior.

Research paper thumbnail of Limit analysis of frames involving unilateral supports with frictional contact

International Journal of Mechanical Sciences, 2007

ABSTRACT We consider the classical limit analysis problem of frame structures made up of rigid pe... more ABSTRACT We consider the classical limit analysis problem of frame structures made up of rigid perfectly plastic members and involving some supports in unilateral frictional contact with the ground. A direct formulation as a mixed complementarity problem (MCP) is used. For the Coulomb case, which forms the focus of this paper, the corresponding MCP may admit multiple upper bound collapse load solutions. In order to identify the least upper bound solution, we propose two algorithms. The first one attempts to enumerate the possible multiple solutions, or at least map the solution space if the solutions are connected. The second scheme tries to find the least upper bound by directly formulating and solving a single nonconvex optimization problem, known in the literature as a mathematical program with equilibrium constraints (MPEC). Two simple examples are provided to illustrate application of these approaches. They also serve to highlight some key features of such structures.

Research paper thumbnail of Performance of the p-version finite element method for limit analysis

International Journal of Mechanical Sciences, 2003

In this paper, we investigate the use of the p-version finite element method in carrying out limi... more In this paper, we investigate the use of the p-version finite element method in carrying out limit analysis using a mathematical programming-based static approach. An important motivation for this study is to overcome the well-known locking behavior—caused by the incompressibility constraint—that may occur in plane strain and 3D problems for such common yield criteria as von Mises’. Quadrilateral elements and

Research paper thumbnail of A constrained non-linear system approach for the solution of an extended limit analysis problem

International Journal for Numerical Methods in Engineering, 2009

A number of recent papers (see, e.g. (Int. have shown that classical limit analysis can be extend... more A number of recent papers (see, e.g. (Int. have shown that classical limit analysis can be extended to incorporate such important features as geometric non-linearity, softening and various so-called ductility constraints. The generic formulation takes the form of a challenging (nonconvex and nonsmooth) optimization problem referred to in the mathematical programming literature as a mathematical program with equilibrium constraints (MPEC). Similar to a classical limit analysis, the aim is to compute in a single step a bound (upper bound, in the case of the extended problem) to the maximum load. The solution algorithm so far proposed to solve the MPEC is to convert it into an iterative non-linear programming problem and attempts to process this using a standard non-linear optimizer. Motivated by the fact that no method is guaranteed to solve such MPECs and by the need to avoid the use of an optimization approach, which is unfamiliar to most practising engineers, we propose, in the present paper, a novel numerical scheme to solve the MPEC as a constrained non-linear system of equations. We illustrate the application of this approach using the simple class of elastoplastic softening skeletal structures for which certain ductility conditions are prescribed.

Research paper thumbnail of Simultaneous ultimate load and deformation analysis of strain softening frames under combined stresses

Engineering Structures, 2008

This paper presents a method for carrying out, in a single step, an elastoplastic analysis to obt... more This paper presents a method for carrying out, in a single step, an elastoplastic analysis to obtain simultaneously both the ultimate load and corresponding deformation of a strain softening structure. The effect of combined bending moment and axial force is also accounted for in the piecewise linearized softening yield condition. However, a monotonic loading process is assumed within a small displacement framework. We propose a mathematical programming approach to tackle this problem. In particular, the formulation leads to an instance of the challenging class of a so-called "mathematical program with equilibrium constraints" (MPEC). Various nonlinear programming based algorithms are proposed to solve the MPEC. Numerical examples are provided to illustrate the described analysis and also to highlight the effects of constitutive local softening instability and of axial forces on the overall structural behavior of the frames.

Research paper thumbnail of Collapse load evaluation of structures with frictional contact supports under combined stresses

Computers & Structures, 2011

ABSTRACT This paper extends classical limit analysis to structures for which some supports are su... more ABSTRACT This paper extends classical limit analysis to structures for which some supports are subjected to “nonstandard” unilateral frictional contact with the ground. A typical and commonly adopted model is nonassociative Coulomb friction. For such cases, the use of the classical bound theorems is not possible. Moreover, simply solving the governing equations as a mixed complementarity problem (MCP) does not guarantee that the best bound has been calculated. We have therefore developed an approach that attempts to compute, in a single step, the critical (least) upper bound solution by formulating and solving an instance of the challenging class of optimization problems, known as a mathematical program with equilibrium constraints (MPEC). Two examples are provided to illustrate application of the proposed scheme, as well as to highlight some key features of such structures.

Research paper thumbnail of Modeling Fracture in Masonry

Journal of Structural Engineering, 2007

A finite element procedure developed for the study of fracture in concrete is extended for the si... more A finite element procedure developed for the study of fracture in concrete is extended for the simulation of tensile and/or shear fracture in masonry. Triangular units are grouped into rectangular zones mimicking brick units with surrounding mortar joints. Fracture is captured through a constitutive softening-fracture law at the boundary interface nodes. The mortar joint, which is a plane of weakness, can be modeled as an interface of zero thickness or of a given thickness. At each nodal location, there exist essentially two nodes, the relative ...

Research paper thumbnail of Nonlinear analysis and buckling of elastically supported circular shallow arches

International Journal of Solids and Structures, 2007

Arches are often supported elastically by other structural members. This paper investigates the i... more Arches are often supported elastically by other structural members. This paper investigates the in-plane nonlinear elastic behaviour and stability of elastically supported shallow circular arches that are subjected to a radial load uniformly distributed around the arch axis. Analytical solutions for the nonlinear behaviour and for the nonlinear buckling load are obtained for shallow arches with equal or unequal elastic supports. It is found that the flexibility of the elastic supports and the shallowness of the arch play important roles in the nonlinear structural response of the arch. The limiting shallownesses that distinguish between the buckling modes are obtained and the relationship of the limiting shallowness with the flexibility of the elastic supports is established, and the critical flexibility of the elastic radial supports is derived. An arch with equal elastic radial supports whose flexibility is larger than the critical value becomes an elastically supported beam curved in elevation, while an arch with one rigid and one elastic radial support whose flexibility is larger than the critical value still behaves as an arch when its shallowness is higher than a limiting shallowness. Comparisons with finite element results demonstrate that the analytical solutions and the values of the critical flexibility of the elastic supports and the limiting shallowness of the arch are valid.

Research paper thumbnail of Non-linear in-plane buckling of rotationally restrained shallow arches under a central concentrated load

International Journal of Non-Linear Mechanics, 2008

Research paper thumbnail of Probabilistic interval analysis for structures with uncertainty

Structural Safety, 2010

A hybrid probabilistic and interval method for engineering problems described by a mixture of ran... more A hybrid probabilistic and interval method for engineering problems described by a mixture of random and interval variables is presented. Random interval arithmetic for carrying out basic operations between random and interval variables is developed by extending interval arithmetic rules. The uncertainty of a random interval variable is represented by probabilistic as well as interval information. A random interval moment method is proposed to calculate the mean and variance of random interval variables. The solution strategy and associated numerical tool are developed by using perturbation theory and Taylor expansion for linear equations with random and interval variables. Engineering applications in structures with analytical or semi-analytical solutions are used to demonstrate the accuracy and effectiveness of the proposed method.

Research paper thumbnail of Optimal tilt lifting of beams as a min-max problem

Structural and Multidisciplinary Optimization, 2004

This paper considers the problem of finding the optimal pickup points for a beam that is to be ti... more This paper considers the problem of finding the optimal pickup points for a beam that is to be tilt lifted by a system of slings attached to a crane. Under the assumptions of a rigid beam and inextensible cables, this task is formulated as a min-max optimization problem. As for its numerical solution, we propose an efficient and robust algorithm involving smoothing and an appropriate discretization of the objective function. A typical numerical example is provided to illustrate the approach.