Computational Mechanics

Compressed sensing is a signal compression technique with very remarkable properties. Among them, maybe the most salient one is its ability of overcoming the Shannon-Nyquist sampling theorem. In other words, it is able to reconstruct a signal at less than 2Q samplings per second, where Q stands for the highest frequency content of the signal. This property has, however, important applications in the field of computational mechanics, as we analyze in this paper. We consider a wide variety of applications, such as model order reduction, manifold learning, data-driven applications and nonlinear dimensionality reduction. Examples are provided for all of them that show the potentialities of compressed sensing in terms of CPU savings in the field of computational mechanics. Compressed sensing • Model order reduction • Manifold learning • Nonlinear dimensionality reduction 1 Introduction Model Order Reduction (MOR) is acquiring an utmost importance for simulation-based engineering. These techniques allow solving efficiently complex mathematical models, thanks to the use of adapted approximation bases to describe their solutions. Among the numerous existing B E. Cueto

The aim of this contribution is a comparison of different mapping techniques usually applied in the field of hierarchical adaptive FE-codes. The calculation of mechanical field variables for the modified mesh is an important but sensitive aspect of adaptation approaches of the spatial discretization. Regarding non-linear boundary value problems procedures of mesh refinement and coarsening imply the determination of strains, stresses and internal variables at the nodes and the Gauss points of new elements based on the transfer of the required data from the former mesh. The kind of mapping of the field variables affects the convergence behaviour as well as the costs of an adaptive FEM-calculation in a non-negligible manner. In order to improve the stability as well as the efficiency of the adaptive process a comparison of different mapping algorithms is presented and evaluated. Within this context, the mapping methods taken into account are -an element-oriented extrapolation procedure using special shape functions, -a patch-oriented transfer approach and, -the allocation of nodal history-dependent state (field) variable data using a supplementary integration of the material law at the nodes of the elements.

The aim of this contribution is a comparison of different mapping techniques usually applied in the field of hierarchical adaptive FE-codes. The calculation of mechanical field variables for the modified mesh is an important but sensitive aspect of adaptation approaches of the spatial discretization. Regarding non-linear boundary value problems procedures of mesh refinement and coarsening imply the determination of strains, stresses and internal variables at the nodes and the Gauss points of new elements based on the transfer of the required data from the former mesh. The kind of mapping of the field variables affects the convergence behaviour as well as the costs of an adaptive FEM-calculation in a non-negligible manner. In order to improve the stability as well as the efficiency of the adaptive process a comparison of different mapping algorithms is presented and evaluated. Within this context, the mapping methods taken into account are -an element-oriented extrapolation procedure using special shape functions, -a patch-oriented transfer approach and, -the allocation of nodal history-dependent state (field) variable data using a supplementary integration of the material law at the nodes of the elements.

The aim of this contribution is the presentation of an adaptive finite element procedure for the solution of geometrically and physically non-linear problems in structural mechanics. Within this context, the attention is mainly directed on the error estimation and hierarchical strategies for mesh refinement and coarsening in the case of finite elasto-plastic deformations. An important but sensitive aspect of adaptation approaches of the space discretization is the calculation of mechanical field variables for the modified mesh. Procedures of mesh refinement and coarsening imply the determination of strains, stresses and internal variables at the nodes and the Gauss points of new elements based on the transfer of the required data from the former mesh. In order to improve the efficiency as well as the convergence behaviour of the adaptive FE process an approach of data transfer primarily related to nodal values is presented. It is characterized by solving the initial value problem not only at the Gauss points but additionally at the nodes of the elements.

We show that in the variational multiscale framework, the weak enforcement of essential boundary conditions via Nitsche's method corresponds directly to a particular choice of projection operator. The consistency, symmetry and penalty terms of Nitsche's method all originate from the fine-scale closure dictated by the corresponding scale decomposition. As a result of this formalism, we are able to determine the exact fine-scale contributions in Nitsche-type formulations. In the context of the advection-diffusion equation, we develop a residual-based model that incorporates the non-vanishing fine scales at the Dirichlet boundaries. This results in an additional boundary term with a new model parameter. We then propose a parameter estimation strategy for all parameters involved that is also consistent for higher-order basis functions. We illustrate with numerical experiments that our new augmented model mitigates the overly diffusive behavior that the classical residual-based fine-scale model exhibits in boundary layers at boundaries with weakly enforced essential conditions.

The aim of this paper is to extend the applicability of an algorithm for solving inconsistent linear systems to the rank-deficient case, by employing incomplete projections onto the set of solutions of the augmented system Axr = b. The extended algorithm converges to the unique minimal norm solution of the least squares solutions. For that purpose, incomplete oblique projections are used, defined by means of matrices that penalize the norm of the residuals. The theoretical properties of the new algorithm are analyzed, and numerical experiences are presented comparing its performance with some well-known projection methods.

Global SLS-resolution is a well-known procedural semantics for top-down computation of queries under the well-founded model. It inherits from SLDNF-resolution the linearity property of derivations, which makes it easy and efficient to implement using a simple stack-based memory structure. However, like SLDNF-resolution it suffers from the problem of infinite loops and redundant computations. To resolve this problem, in this paper we develop a new procedural semantics, called SLTNF-resolution, by enhancing Global SLS-resolution with loop cutting and tabling mechanisms. SLTNFresolution is sound and complete w.r.t. the well-founded semantics for logic programs with the bounded-term-size property, and is superior to existing linear tabling procedural semantics such as SLT-resolution.

The extended finite element method combines the flexibility of mesh-independent discontinuities and the accuracy of singular enrichment functions. This paper introduces the method in the context of linear elasticity and gives an overview of its current state of research.

A parallel edge-based solution of three dimensional viscoplastic flows governed by the steady Navier-Stokes equations is presented. The governing partial differential equations are discretized using the SUPG/PSPG stabilized finite element method on unstructured grids. The highly nonlinear algebraic system arising from the convective and material effects is solved by an inexact Newton-Krylov method. The locally linear Newton equations are solved by GMRES with nodal block diagonal preconditioner. Matrix-vector products within GMRES are computed edge-by-edge (EDE), diminishing flop counts and memory requirements. A comparison between EDE and element-by-element data structures is presented. The parallel computations were based in a message passing interface standard. Performance tests were carried out in representative three dimensional problems, the sudden expansion for power-law fluids and the flow of Bingham fluids in a lid-driven cavity. Results have shown that edge based schemes requires less CPU time and memory than elementbased solutions.

The failure of engineering structures can have catastrophic consequences, leading to significant economic losses-both material and financial-and, in some cases, loss of human lives. Such failures often occur due to inadequate determination of structural loads or when materials exceed their yield strength, causing excessive deformation. This study revisits von Mises' theory and presents a newly formulated general applied stress mathematical model. Polynomial displacement shape profiles were employed to evaluate n-values for different plate types, leading to the derivation of n-value equations. Additionally, new general applied stress equations, Stress Factor (Fss), equations for shear strain energy theory for various boundary conditions, and allowable stress equations were developed. Validation of the newly formulated equations revealed that the applied stress values exceeded the yield stress of structural steel for plates with one free edge. To mitigate potential failure, a safety factor of 1.15 was introduced for the plate types considered which reduces the applied stress of 281N/mm2 to allowable stress of 244N/mm2 below the material yield stress of 250N/mm2. The results obtained align with findings from existing literature, confirming the reliability of the developed equations. As such, the new equations provide an effective means of predicting the allowable stress of plane materials based on the maximum shear strain energy theory.

Modern industrial standards require advanced constitutive modeling to obtain satisfactory numerical results. This approach however, is causing significant increase in number of material parameters which can not be easily obtained from standard and commonly known experimental techniques. Therefore, it is desirable to introduce procedure decreasing the number of the material parameters. This reduction however, should not lead to misunderstanding the fundamental physical phenomena. This paper proposes the reduction of the number of material parameters by using ANN approximation. Recently proposed viscoplasticity formulation for anisotropic solids (metals) developed by authors is used as an illustrative example. In this model one needs to identify 28 material parameters to handle particular metal behaviour under adiabatic conditions as reported by Glema et al (

In this paper the numerical implementation of two-scale modelling of bone microstructure is presented. The study is a part of long-term project on bone remodelling which drives bone microstructure change based directly on trabeculae surface energy. The proposed approach is based on a first-order computational homogenization technique. The coincidence of macro-and micro-model kinematics is done with the use of uniform displacement and traction boundary conditions. The computational homogenization procedure is driven by a self-prepared manager which is coded in Python. The computation on real bone structure (a piece of female Wistar rat bone) is performed as well.

In this paper the numerical implementation of two-scale modelling of bone microstructure is presented. The study is a part of long-term project on bone remodelling which drives bone microstructure change based directly on trabeculae surface energy. The proposed approach is based on a first-order computational homogenization technique. The coincidence of macro-and micro-model kinematics is done with the use of uniform displacement and traction boundary conditions. The computational homogenization procedure is driven by a self-prepared manager which is coded in Python. The computation on real bone structure (a piece of female Wistar rat bone) is performed as well.

Modern industrial standards require advanced constitutive modeling to obtain satisfactory numerical results. This approach however, is causing significant increase in number of material parameters which can not be easily obtained from standard and commonly known experimental techniques. Therefore, it is desirable to introduce procedure decreasing the number of the material parameters. This reduction however, should not lead to misunderstanding the fundamental physical phenomena. This paper proposes the reduction of the number of material parameters by using ANN approximation. Recently proposed viscoplasticity formulation for anisotropic solids (metals) developed by authors is used as an illustrative example. In this model one needs to identify 28 material parameters to handle particular metal behaviour under adiabatic conditions as reported by Glema et al (

The main objective of the present paper is the numerical investigation of dynamic shear bands in inelastic solids generated by impact-loaded adiabatic processes. Particular attention is focused on the proper description of a ductile mode propagating along the shear band for high impact velocities.

Before isogeometric analysis can be applied to solving a partial differential equation posed over some physical domain, one needs to construct a valid parametrization of the geometry. The accuracy of the analysis is affected by the quality of the parametrization. The challenge of computing and maintaining a valid geometry parametrization is particularly relevant in applications of isogemetric analysis to shape optimization, where the geometry varies from one optimization iteration to another. We propose a general framework for handling the geometry parametrization in isogeometric analysis and shape optimization. It utilizes an expensive non-linear method for constructing/updating a high quality reference parametrization, and an inexpensive linear method for maintaining the parametrization in the vicinity of the reference one. We describe several linear and non-linear parametrization methods, which are suitable for our framework. The non-linear methods we consider are based on solving a constrained optimization problem numerically, and are divided into two classes, geometry-oriented methods and analysisoriented methods. Their performance is illustrated through a few numerical examples.

We consider the benchmark problem of magnetic energy density enhancement in a small spatial region by varying the shape of two symmetric conducting scatterers. We view this problem as a prototype for a wide variety of geometric design problems in electromagnetic applications. Our approach for solving this problem is based on shape optimization and isogeometric analysis. One of the major difficulties we face to make these methods work together is the need to maintain a valid parametrization of the computational domain during the optimization. Our approach to generating a domain parametrization is based on minimizing a second order approximation to the Winslow functional in the vicinity of a reference parametrization. Furthermore, we enforce the validity of the parametrization by ensuring the non-negativity of the coefficients of a B-spline expansion of the Jacobian. The shape found by this approach outperforms earlier design computed using topology optimization by a factor of one billion.

We consider a model problem of isogeometric shape optimization of vibrating membranes whose shapes are allowed to vary freely. The main obstacle we face is the need for robust and inexpensive extension of a B-spline parametrization from the boundary of a domain onto its interior, a task which has to be performed in every optimization iteration. We experiment with two numerical methods (one is based on the idea of constructing a quasi-conformal mapping, whereas the other is based on a spring-based mesh model) for carrying out this task, which turn out to work sufficiently well in the present situation. We perform a number of numerical experiments with our isogeometric shape optimization algorithm and present smooth, optimized membrane shapes. Our conclusion is that isogeometric analysis fits well with shape optimization.

A new set of benchmarks has been developed for the performance evaluation of highly parallel supercomputers. These benchmarks consist of ve \parallel kernel" benchmarks and three \simulated application" benchmarks. Together they mimic the computation and data movement c haracteristics of large scale computational uid dynamics applications. The principal distinguishing feature of these benchmarks is their \pencil and paper" speci cation | all details of these benchmarks are speci ed only algorithmically. In this way m a n y of the di culties associated with conventional benchmarking approaches on highly parallel systems are avoided.

HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L'archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

O keep readers up-to-date with what's happening in other publications by Computational Mechanics, we follow here with a list of some recent papers published in our group of international journals. All our journals are published quarterly and subscription enquiries should be sent to the appropriate address on the front page of this issue.

We show that the behavior of T700/M21s and T800/M21s composite panels are affected by the influence of strain rates together with local shear and crush punch or global flexural strengths of the structure. A deterministic continuous composite material model has been developed as a LS-DYNA user defined material model for unidirectional composites on the basis of the Matzenmiller model widely used for woven composites. Initiation and evolution up to saturation and fracture are implemented for various and coupled damage mechanisms including delamination. Quasi-static and dynamic characterization tests laminates have been carried out on balanced angle ply [±θ] and used for calibration of numerical values. Impact induced damage from experiment’s measures and numerical predictions are compared for T800/M21S aeronautical samples impacted at 15J.

The extended finite element method (X-FEM) has been developed to minimize requirements on the mesh in a problem with a displacement discontinuity. We present the development carried out to take advantage of the X-FEM approach in simplifying the meshing of complex 3D networks of discontinuities with junctions. Contact with large sliding along the branched discontinuities is discussed. Solutions are proposed and discussed to solve some matrix conditioning issues. Several examples are presented in this paper in order to prove the efficiency of the proposed approach.

This paper presents an energetic approach to compute mixed mode stress intensity factors (SIFs) along a crack front in linear thermo-elasticity, for meshed or non-meshed cracks. This formulation considers the energy release rate as a symmetric bilinear form of the displacement field and use the explicit expressions of the singular displacements known for a plane strain and anti-plane crack in linear elasticity. We explain how to compute this bilinear form with an extension of the "G-theta" method for a linear thermo-elastic problem in 3D. This method introduces a virtual crack extension velocity field. We focus on how this virtual field is applied on a virtual tore around the crack front. We describe how the discretization and the computation of the energy release rate and the SIFs can be implemented within a general-purpose finite element code. The finite element program Code_Aster  , a free software under GPL license is considered in this study. This approach keeps the advantages of the other methods to determine the SIFs (domain integrals, crack tip contour integrals) without the constraint of an integration box definition, since the formulation is more global. Moreover, the crack is represented by level sets. A local basis at the crack tip can be defined easily within this representation, in which the singular fields can be expressed. This paper includes illustrative examples showing the accuracy of the method. Comparisons with exact solutions prove the efficiency and the robustness of the present formulation for planar crack problems.

This work focuses on the development of a super-penalty strategy based on the L 2 -projection of suitable coupling terms to achieve C 1 -continuity between non-conforming multi-patch isogeometric Kirchhoff plates. In particular, the choice of penalty parameters is driven by the underlying perturbed saddle point problem from which the Lagrange multipliers are eliminated and is performed to guarantee the optimal accuracy of the method. Moreover, by construction, the method does not suffer from boundary locking, especially on very coarse meshes. We demonstrate the applicability of the proposed coupling algorithm to Kirchhoff plates by studying several benchmark examples discretized by non-conforming meshes. In all cases, we recover the optimal rates of convergence achievable by B-splines where we achieve a substantial gain in accuracy per degree-of-freedom compared to other choices of the penalty parameters. Isogeometric analysis • Multi-patch coupling • Super-penalty method • Kirchhoff plates B Luca Coradello

This work focuses on the development of a super-penalty strategy based on the $$L^2$$ L 2 -projection of suitable coupling terms to achieve $$C^1$$ C 1 -continuity between non-conforming multi-patch isogeometric Kirchhoff plates. In particular, the choice of penalty parameters is driven by the underlying perturbed saddle point problem from which the Lagrange multipliers are eliminated and is performed to guarantee the optimal accuracy of the method. Moreover, by construction, the method does not suffer from boundary locking, especially on very coarse meshes. We demonstrate the applicability of the proposed coupling algorithm to Kirchhoff plates by studying several benchmark examples discretized by non-conforming meshes. In all cases, we recover the optimal rates of convergence achievable by B-splines where we achieve a substantial gain in accuracy per degree-of-freedom compared to other choices of the penalty parameters.

In this paper we will present Eldi, a mobile robot that has been in daily operation at the Elder Museum of S ien e and Te hnology at Las Palmas de Gran Canaria sin e De ember 1999. The system that ontrols Eldi and the rest of the installation has been on eived as a set of agents that intera t by means of dis rete events. This is an ongoing proje t that was organized in three di erent stages of whi h only the rst one has been a omplished termed The Player. This paper will des ribe brie y the physi al robot, the environment and demos developed. Finally, we will summarize some important lessons learnt.

For intra-cavity laser beam control, a small, low-cost deformable mirror is required. This mirror can be used to correct for time-dependent phase aberrations to the laser beam, such as those caused by thermal expansion of materials. A piezoelectric unimorph design is suitable for this application. The proposed unimorph consists of a copper disc with mirror finish, bonded to a piezoelectric disc. The deformations that the mirror is required to perform are routinely (at least in optical applications) described using Zernike polynomials, which are a complete set of orthogonal functions defined on a unit disc. The challenge is to design a device that can represent selected polynomials as accurately as possible with a specified amplitude. To assist in the design process, numerical modelling is required to predict the deformation shapes that can be achieved by a unimorph mirror with a particular electrode pattern. In this paper a previously proposed axisymmetric Rayleigh-Ritz formulation, is extended to account for non-axisymmetric voltage distributions, and therefore non-axisymmetric displacements. The Rayleigh-Ritz model, which uses the Zernike polynomials directly to describe the displacements, produced a small model (stiffness matrix dimension equal to the number of polynomials used) that predicts the deformations of the piezoelectric mirror with remarkable accuracy. The results using this Rayleigh-Ritz formulation are compared to results from a traditional finite element analysis using a commercial finite element package. Both numerical models were applied to model a prototype deformable mirror and produced good agreement with experimental results.

HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L'archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

In this paper, elasto-plastic analysis of an edge crack has been performed using element free Galerkin method. A model problem has been solved in plane stress condition under mode-I loading. A system of nonlinear equations has been obtained by using incremental theory of plasticity, and the equations are solved by assuming piecewise linear approximation. A code has been written in Matlab for elastoplastic analysis of cracked components. The size of plastic zone is calculated around the tip of the crack by EFGM code.

We introduce a class of simple models for shear thickening and/ or 'jamming' in colloidal suspensions. These are based on schematic mode coupling theory (MCT) of the glass transition, having a memory term that depends on a density variable, and on both the shear stress and the shear rate. (Tensorial aspects of the rheology, such as normal stresses, are ignored for simplicity.) We calculate steady-state flow curves and correlation functions. Depending on model parameters, we find a range of rheological behaviours, including 'S-shaped' flow curves, indicating discontinuous shear thickening, and stress-induced transitions from a fluid to a nonergodic (jammed) state, showing zero flow rate in an interval of applied stress. The shear thickening and jamming scenarios that we explore appear broadly consistent with experiments on dense colloids close to the glass transition, despite the fact that we ignore hydrodynamic interactions. In particular, the jamming transition we propose is conceptually quite different from various hydrodynamic mechanisms of shear thickening in the literature, although the latter might remain pertinent at lower colloid densities. Our jammed state is a stress-induced glass, but its nonergodicity transitions have an analytical structure distinct from that of the conventional MCT glass transition.

We advocate the use of an explicit time representation in syntactic pattern recognition because it can result in more succinct models and easier learning problems. We apply this approach to the real-world problem of learning models for the driving behavior of truck drivers. We discretize the values of onboard sensors into simple events. Instead of the common syntactic pattern recognition approach of sampling the signal values at a fixed rate, we model the time constraints using timed models. We learn these models using the RTI+ algorithm from grammatical inference, and show how to use computational mechanics and a form of semi-supervised classification to construct a real-time automaton classifier for driving behavior. Promising results are shown using this new approach.

A smoothed particle hydrodynamics (SPH) solution to the Rayleigh-Taylor instability (RTI) problem in an incompressible viscous two-phase immiscible fluid with surface tension is presented. The present model is validated by solving Laplace's law, and square bubble deformation without surface tension whereby it is shown that the implemented SPH discretization does not produce any artificial surface tension. To further validate the numerical model for the RTI problem, results are quantitatively compared with analytical solutions in a linear regime. It is found that the SPH method slightly overestimates the border of instability. The long time evolution of simulations is presented for investigating changes in the topology of rising bubbles and falling spike in RTI, and the computed Froude numbers are compared with previous works. It is shown that the numerical algorithm used in this work is capable of capturing the interface evolution and growth rate in RTI accurately. Smoothed particle hydrodynamics (SPH) • Mesh free method • Projection method • Multi-phase flow • Interfacial flow • Rayleigh-Taylor instability (RTI)

• Multi-objective optimization of composite plates is performed using lamination parameters. • Fundamental frequency, buckling load and effective stiffness metrics are maximized. • Pareto-optimal solutions are determined considering various problem cases. • A valuable insight has been provided on conformity/conflict of multiple objectives. • Presented methodology can be utilized for the optimal design of laminated plates.

An approach combining the method of fundamental solutions (MFS) in conjunction with the normal modes technique (NMT) is proposed to simulate the acoustic wave propagation over the shallow water region. It is assumed that the sound-speed of considered model is the isovelocity profile, the free surface is quiescent and the seabed is rugged. The seabed, ranging from smooth to abrupt variation, is discretized into simple rectangular geometry and tunnel-shape deformation at the seabed in terms of the irregular topography. Mathematical formulations of the eigenfunction expansion, in point of NMT, are implemented clearly to describe the radiation conditions on the open boundaries. Effects of node resolution, numbers of modes on open boundaries and small aspect ratios over the computational domain are discussed. Accuracy of the results by the proposed method is assessed and verified by comparison with analytic solution and the boundary element method (BEM). Through the study, the dominant of transmission of energy under sources excitation beyond the underwater acoustic model is analyzed. It appears that the MFS is very effective for acoustic wave propagation problem.

A meshless Element-Free Galerkin (EFG) equilibrium formulation is proposed to compute the limit loads which can be sustained by plates and slabs. In the formulation pure moment fields are approximated using a moving least squares technique, which means that the resulting fields are smooth over the entire problem domain. There is therefore no need to enforce continuity conditions at interfaces within the problem domain, which would be a key part of a comparable finite element formulation. The collocation method is used to enforce the strong form of the equilibrium equations and a stabilized conforming nodal integration scheme is introduced to eliminate numerical instability problems. The combination of the collocation method and the smoothing technique means that equilibrium only needs to be enforced at the nodes, and stable and accurate solutions can be obtained with minimal computational effort. The von Mises and Nielsen yield criteria which are used in the analysis of plates and slabs respectively are enforced by introducing second-order cone constraints, ensuring that the resulting optimization problem can be solved using efficient interior-point solvers. Finally, the efficacy of the procedure is demonstrated by applying it to various benchmark plate and slab problems.

This paper presents a new numerical procedure for kinematic limit analysis problems, which incorporates the cell-based smoothed finite element method (CS-FEM) with second-order cone programming. The application of a strain smoothing technique to the standard displacement finite element both rules out volumetric locking and also results in an efficient method that can provide accurate solutions with minimal computational effort. The non-smooth optimization problem is formulated as a problem of minimizing a sum of Euclidean norms, ensuring that the resulting optimization problem can be solved by an efficient second order cone programming algorithm. Plane stress and plane strain problems governed by the von Mises criterion are considered, but extensions to problems with other yield criteria having a similar conic quadratic form or 3D problems can be envisaged.

The meshless Element-Free Galerkin (EFG) method is extended to allow computation of the limit load of plates. A kinematic formulation which involves approximating the displacement/velocity field using the moving least squares technique is developed. Only one displacement variable is required for each EFG node, ensuring that the total number of variables in the resulting optimization problem is kept to a minimum, with far fewer variables being required compared with finite element formulations. A stabilized conforming nodal integration scheme is extended to plastic plate bending problems. The evaluation of integrals at nodal points using curvature smoothing stabilization both keeps the size of the optimization problem small and also results in stable and accurate solutions. Difficulties imposing essential boundary conditions are overcome by enforcing directly displacements at the nodes. The formulation can be expressed as the problem of minimizing a sum of Euclidean norms subject to a set of equality constraints. This non-smooth minimization problem can be transformed into a form suitable for solution using Second-Order Cone Programming (SOCP). The procedure is applied to several benchmark problems and is found in practice to generate good upper bound solutions for benchmark problems.