D. Lloyd Smith

An efficient beam-column formulation for 3D reinforced concrete frames

Abstract This paper presents a new beam–column formulation which can be used for the accurate, yet efficient, modelling of 3D reinforced concrete (R/C) frames. The formulation is intended for modelling the nonlinear elastic behaviour of a whole R/C beam–column with only one element, which is an essential ingredient of adaptive elasto-plastic analysis. On the longitudinal axis level, quartic shape functions are used to represent the two transverse displacements. A constant axial force criterion is employed instead of shape functions for the axial displacement, which is largely responsible for the accuracy of the proposed formulation. For concrete, the formulation assumes a nonlinear compressive stress–strain relationship and no tensile resistance; whereas for steel, a linear stress–strain relationship is utilised. On the cross-sectional level, the formulation is capable of modelling the interaction between the axial force and the biaxial moments for a general R/C cross-section, with explicit expressions obtained using a novel approach based on integration over triangular subdomains. The paper provides the details of the proposed formulation, and presents several verification examples to demonstrate the accuracy of this formulation and its ability to model the nonlinear elastic response of reinforced concrete beam–columns with only one element per member.

Efficient nonlinear analysis of elasto-plastic 3D R/C frames using adaptive techniques

Abstract This paper presents a new nonlinear analysis method for three-dimensional reinforced concrete (R/C) frames employing adaptive analysis concepts. The first two components of the proposed adaptive method, namely the elastic and elasto-plastic beam–column formulations, are described. The details of automatic mesh refinement, which is the third component of the adaptive method, are then presented. These include the construction of an effective interaction surface representing generalised stress states at the elastic limit, the determination and checking of generalised stresses for exceeding the elastic limit along an elastic element, and the refinement of an elastic element into an appropriate number of elastic and elasto-plastic elements. Examples are finally presented to illustrate the accuracy and efficiency of the proposed analysis method.

Plastic Limit Analysis

Systematic mesh and nodal descriptions of the laws of statics and kinematics for the limiting state of plastic collapse in a structural system are set out. Then the constitutive relations appropriate to this condition are presented in such a way as to emphasise their inherent complementarity. The mixing together of these three independent ingredients — statics, kinematics and material constitution — gives rise to the vectorial formulation which governs plastic collapse: it is identified as a linear complementarity problem. From it are derived the dual linear programs which give expression to the variational principles associated with upper and lower bounds on the collapse load factor.

Statics and Kinematics

The statics and kinematics of simple framed structures are presented in the setting of small displacements and deformations. Firstly, the similarity of mathematical form between structural mechanics and other engineering problems is expressed in terms of network theory, and this approach is used to emphasise the need for a systematic description of the structural problem. Two, quite different, but equally systematic ways of setting out the static and kinematic laws are suggested: the mesh and nodal descriptions. A guiding adjoint formalism — static-kinematic duality — is seen to pervade the mathematical representation of statics and kinematics, and this contributes to the considerable symmetry in formulations of structural problems. For improved data generation, the nodal description is presented in system coordinates, a procedure for assembling a mesh description for frames with rectangular meshes is suggested, and the transformation of nodal into mesh equilibrium equations is mentioned.

Fuzzy Linear Programming in Plastic Limit Design

Plastic limit design entails the designing of a structure so that it will just reach the limit state of plastic collapse under prescribed design loads, and, in addition, so that some design objective, often relating to weight or cost, is optimally achieved. When the geometry of the structure is fixed a priori, the design loading is known with complete precision and the objective function is linear, the problem can be expressed as one of linear programming.

Explaining design plans

The paper describes a methodology for generating quality explanations from design plans. In selecting items of information for inclusion in an explanation, the methodology considers the rationales behind the strategic knowledge and object-level knowledge specified in a design plan. Rhetorical structure theory and discourse focus tracking are utilised to determine textual structure, and to maintain discourse coherence and cohesion. Using a simple system of user modelling, it is shown how the methodology flexibly includes consideration of a users knowledge, thus resulting in more focused and convincing explanations. The methodology is used to investigate follow-up explanations, and the generation of explanations from plans which contain a misconception on the part of the designer.

Rigid Plastic Dynamics

The problem of rigid-plastic framed structures subjected to load pulses of arbitrary form, and of intensity such that substantial plastic deformation takes place, is treated by approximate means. The investigation is restricted to the range of low intensity excitation which induces a global dynamic response.

Metaknowledge reasoning in civil engineering expert systems

Abstract The ability of a Civil Engineering Expert System to utilize in an intelligent manner the knowledge it possesses is a feature still sadly lacking in most present-day working systems. A system designed for a civil engineering application tends to attract an extensive knowledge base; the size of the base therefore demands selective use of its contents for efficient decision making. This paper presents a simple, yet potentially powerful, method of enabling metaknowledge reasoning within a logic/procedural programming environment for civil engineering expert system applications, with minimum repair work to existing data structures. Examples of the use of the approach are presented using some preliminary design knowledge. Limitations and possible future extensions to this approach are also discussed.

Quadratic Programs and Complementarity

The optimality criteria associated with a convex minimising quadratic program are shown to form a special type of linear complementarity problem, one that has a symmetric matrix. The dual quadratic programs of Dorn are derived, as are the symmetric dual programs of Cottle which are especially useful in elasto-plastic structural analysis. Cottle’s duality theorem is stated, and attention is given to the joint solution and to the question of uniqueness of solution. Wolfe’s algorithm for solving quadratic programs is discussed. The Wolfe-Markowitz algorithm for solving a parametric quadratic program is introduced, and its use in solving the parametric linear complementarity problem associated with elasto-plastic structural analysis is described.