Related papers: A Complete Graphic Statics for Rigid-Jointed 3D Fr…

This paper extends graphic statics by describing the forces and moments in any 3D rigid-jointed frame structure in terms of cell complexes using homology theory of algebraic topology. Graphic statics provides a highly geometric way to…

In Part 3 of this sequence of papers, the kinematic behaviour of 3D frame structures is described using the loop formalism that was developed in Part 2 to describe equilibrium. There, the notions of polygons, polyhedra and polytopes that…

This research provides algorithms and numerical methods to geometrically control the magnitude of the internal and external forces in the reciprocal diagrams of 3D/Polyhedral Graphic statics (3DGS). In 3DGS, the form of the structure and…

One of the most influential early works in graphic statics is one of Maxwell, where he introduced the idea of a discontinuous stress function and the use of a 3D projective polarity for a planar problem. A recent work gave an analytical…

Residual stresses are self-equilibrated stresses on unloaded bodies. Owing to their complex origins, it is useful to develop functions that can be linearly combined to represent any sufficiently regular residual stress field. In this work,…

In structural rigidity, one studies frameworks of bars and joints in Euclidean space. Such a framework is an articulated structure consisting of rigid bars, joined together at joints around which the bars may rotate. In this paper, we will…

Using homological techniques we show that a pin-anchored frame that involves only moments and shears provides a conceptual bridge between the statics of moment frames and the kinematics of pin-jointed trusses. One immediate result is a long…

We present a minimalistic approach to simulations of force transmission through granular systems. We start from a configuration containing cohesive (tensile) contact forces and use an adaptive procedure to find the stable configuration with…

This article develops a unified variational framework for configurational (or material) forces in both Classical (3D, non-relativistic) and Relativistic (4D) Continuum Mechanics. Configurational forces describe the evolution of material…

The fundamental ideas and tools of the global geometric formulation of stress and hyper-stress theory of continuum mechanics are introduced. The proposed framework is the infinite dimensional counterpart of statics of systems having finite…

The dynamics of wire frame particles in concentrated suspension are studied by means of a 2D model and compared to those of rod-like particles. The wire frames have bent or branched structures constructed from infinitely thin rigid rods. In…

The mechanical problem discussed in this paper focuses on the stress state estimation in a composite laminate in the vicinity of a free edge or microcracks. To calculate these stresses, we use two models called Multiparticle Models of…

Arterial tissue consists of multiple structurally important constituents that have individual material properties and associated stress-free configurations that evolve over time. This gives rise to residual stresses contributing to the…

A bar framework in R^r, denoted by G(p), is a simple connected graph G whose vertices are points p^1,...,p^n in R^r that affinely span R^r, and whose edges are line segments between pairs of these points. In this paper, we use stress…

A family of mixed finite elements is proposed for solving the first order system of linear elasticity equations in any space dimension, where the stress field is approximated by symmetric finite element tensors. This family of elements has…

Classical field theories together with the Lagrangian and Eulerian approaches to continuum mechanics are embraced under a geometric setting of a fiber bundle. The base manifold can be either the body manifold of continuum mechanics, space…

Using the Lagrangian transport analysis for the turbulence momentum, the Reynolds stress gradient can be expressed as a function of the local momentum flux and force terms. From this perspective of an observer moving at the local mean…

Stress-stress correlations in crystalline solids with long-range order can be straightforwardly derived using elasticity theory. In contrast, the `emergent elasticity' of amorphous solids, rigid materials characterized by an underlying…

Unlike classical elasticity, where stresses arise from deformations relative to a stress-free reference configuration, rigidity in amorphous systems is maintained by disordered force networks that generate internal prestress. Previously, we…

We present a technique for simultaneous 3D reconstruction of static regions and rigidly moving objects in a scene. An RGB-D frame is represented as a collection of features, which are points and planes. We classify the features into static…