Proceedings of the 3rd Annual Conference on Aerospace Computational Control, volume 1

Conference topics included definition of tool requirements, advanced multibody component representation descriptions, model reduction, parallel computation, real time simulation, control design and analysis software, user interface issues, testing and verification, and applications to spacecraft, robotics, and aircraft

A Variational Formulation of Dissipative Quasicontinuum Methods

Lattice systems and discrete networks with dissipative interactions are successfully employed as meso-scale models of heterogeneous solids. As the application scale generally is much larger than that of the discrete links, physically relevant simulations are computationally expensive. The QuasiContinuum (QC) method is a multiscale approach that reduces the computational cost of direct numerical simulations by fully resolving complex phenomena only in regions of interest while coarsening elsewhere. In previous work (Beex et al., J. Mech. Phys. Solids 64, 154-169, 2014), the originally conservative QC methodology was generalized to a virtual-power-based QC approach that includes local dissipative mechanisms. In this contribution, the virtual-power-based QC method is reformulated from a variational point of view, by employing the energy-based variational framework for rate-independent processes (Mielke and Roub\'i\v{c}ek, Rate-Independent Systems: Theory and Application, Springer-Verlag, 2015). By construction it is shown that the QC method with dissipative interactions can be expressed as a minimization problem of a properly built energy potential, providing solutions equivalent to those of the virtual-power-based QC formulation. The theoretical considerations are demonstrated on three simple examples. For them we verify energy consistency, quantify relative errors in energies, and discuss errors in internal variables obtained for different meshes and two summation rules.Comment: 38 pages, 21 figures, 4 tables; moderate revision after review, one example in Section 5.3 adde

Bias extension test for pantographic sheets: numerical simulations based on second gradient shear energies

We consider a bi-dimensional sheet consisting of two orthogonal families of inextensible fibres. Using the representation due to Rivlin and Pipkin for admissible placements, i.e. placements preserving the lengths of the inextensible fibres, we numerically simulate a standard bias extension test on the sheet, solving a non-linear constrained optimization problem. Several first and second gradient deformation energy models are considered, depending on the shear angle between the fibres and on its gradient, and the results obtained are compared. The proposed numerical simulations will be helpful in designing a systematic experimental campaign aimed at characterizing the internal energy for physical realizations of the ideal pantographic structure presented in this paper

Proceedings of the Fifth NASA/NSF/DOD Workshop on Aerospace Computational Control

The Fifth Annual Workshop on Aerospace Computational Control was one in a series of workshops sponsored by NASA, NSF, and the DOD. The purpose of these workshops is to address computational issues in the analysis, design, and testing of flexible multibody control systems for aerospace applications. The intention in holding these workshops is to bring together users, researchers, and developers of computational tools in aerospace systems (spacecraft, space robotics, aerospace transportation vehicles, etc.) for the purpose of exchanging ideas on the state of the art in computational tools and techniques

기하학적으로 정밀한 비선형 구조물의 아이소-지오메트릭 형상 설계 민감도 해석

학위논문 (박사)-- 서울대학교 대학원 : 공과대학 조선해양공학과, 2019. 2. 조선호.In this thesis, a continuum-based analytical adjoint configuration design sensitivity analysis (DSA) method is developed for gradient-based optimal design of curved built-up structures undergoing finite deformations. First, we investigate basic invariance property of linearized strain measures of a planar Timoshenko beam model which is combined with the selective reduced integration and B-bar projection method to alleviate shear and membrane locking. For a nonlinear structural analysis, geometrically exact beam and shell structural models are basically employed. A planar Kirchhoff beam problem is solved using the rotation-free discretization capability of isogeometric analysis (IGA) due to higher order continuity of NURBS basis function whose superior per-DOF(degree-of-freedom) accuracy over the conventional finite element analysis using Hermite basis function is verified. Various inter-patch continuity conditions including rotation continuity are enforced using Lagrage multiplier and penalty methods. This formulation is combined with a phenomenological constitutive model of shape memory polymer (SMP), and shape programming and recovery processes of SMP structures are simulated. Furthermore, for shear-deformable structures, a multiplicative update of finite rotations by an exponential map of a skew-symmetric matrix is employed. A procedure of explicit parameterization of local orthonormal frames in a spatial curve is presented using the smallest rotation method within the IGA framework. In the configuration DSA, the material derivative is applied to a variational equation, and an orientation design variation of curved structure is identified as a change of embedded local orthonormal frames. In a shell model, we use a regularized variational equation with a drilling rotational DOF. The material derivative of the orthogonal transformation matrix can be evaluated at final equilibrium configuration, which enables to compute design sensitivity using the tangent stiffness at the equilibrium without further iterations. A design optimization method for a constrained structure in a curved domain is also developed, which focuses on a lattice structure design on a specified surface. We define a lattice structure and its design variables on a rectangular plane, and utilize a concept of free-form deformation and a global curve interpolation to obtain an analytical expression for the control net of the structure on curved surface. The material derivative of the analytical expression eventually leads to precise design velocity field. Using this method, the number of design variables is reduced and design parameterization becomes more straightforward. In demonstrative examples, we verify the developed analytical adjoint DSA method in beam and shell structural problems undergoing finite deformations with various kinematic and force boundary conditions. The method is also applied to practical optimal design problems of curved built-up structures. For example, we extremize auxeticity of lattice structures, and experimentally verify nearly constant negative Poisson's ratio during large tensile and compressive deformations by using the 3-D printing and optical deformation measurement technologies. Also, we architect phononic band gap structures having significantly large band gap for mitigating noise in low audible frequency ranges.본 연구에서는 대변형을 고려한 휘어진 조립 구조물의 연속체 기반 해석적 애조인 형상 설계 민감도 해석 기법을 개발하였다. 평면 Timoshenko 빔의 선형화된 변형률의 invariance 특성을 고찰하였고 invariant 정식화를 선택적 축소적분(selective reduced integration) 기법 및 B-bar projection 기법과 결합하여 shear 및 membrane 잠김 현상을 해소하였다. 비선형 구조 모델로서 기하학적으로 정밀한 빔 및 쉘 모델을 활용하였다. 평면 Kirchhoff 빔 모델을 NURBS 기저함수의 고차 연속성에 따른 아이소-지오메트릭 해석 기반 rotation-free 이산화를 활용하여 다루었으며, 기존의 Hermite 기저함수 기반의 유한요소법에 비해 자유도당 해의 정확도가 높음을 검증하였다. 라그랑지 승수법 및 벌칙 기법을 도입하여 회전의 연속성을 포함한 다양한 다중패치간 연속 조건을 고려하였다. 이러한 기법을 현상학적 (phenomenological) 형상기억폴리머 (SMP) 재료 구성방정식과 결합하여 형상의 프로그래밍과 회복 과정을 시뮬레이션하였다. 전단변형을 겪는 (shear-deformable) 구조 모델에 대하여 대회전의 갱신을 교대 행렬의 exponential map에 의한 곱의 형태로 수행하였다. 공간상의 곡선 모델에서 최소회전 (smallest rotation) 기법을 통해 국소 정규직교좌표계의 명시적 매개화를 수행하였다. 형상 설계 민감도 해석을 위하여 전미분을 변분 방정식에 적용하였으며 휘어진 구조물의 배향 설계 변화는 국소 정규직교좌표계의 회전에 의하여 기술된다. 최종 변형 형상에서 직교 변환 행렬의 전미분을 계산함으로써 대회전 문제에서 추가적인 반복 계산없이 변형 해석에서의 접선강성행렬에 의해 해석적 설계 민감도를 계산할 수 있다. 쉘 구조물의 경우 면내 회전 자유도 및 안정화된 변분 방정식을 활용하여 보강재(stiffener)의 모델링을 용이하게 하였다. 또한 본 연구에서는 휘어진 영역에 구속되어있는 구조물에 대한 설계 속도장 계산 및 최적 설계기법을 제안하며 특히 곡면에 구속된 빔 구조물의 설계를 집중적으로 다룬다. 자유형상변형(Free-form deformation)기법과 전역 곡선 보간기법을 활용하여 직사각 평면에서 형상 및 설계 변수를 정의하고 곡면상의 곡선 형상을 나타내는 조정점 위치를 해석적으로 표현할 수 있으며 이의 전미분을 통해 정확한 설계속도장을 계산한다. 이를 통해 설계 변수의 개수를 줄일 수 있고 설계의 매개화가 간편해진다. 개발된 방법론은 다양한 하중 및 운동학적 경계조건을 갖는 빔과 쉘의 대변형 문제를 통해 검증되며 여러가지 휘어진 조립 구조물의 최적 설계에 적용된다. 대표적으로, 전단 강성 및 충격 흡수 특성과 같은 기계적 물성치의 개선을 위해 활용되는 오그제틱 (auxetic) 특성이 극대화된 격자 구조를 설계하며 인장 및 압축 대변형 모두에서 일정한 음의 포아송비를 나타냄을 3차원 프린팅과 광학적 변형 측정 기술을 이용하여 실험적으로 검증한다. 또한 우리는 소음의 저감을 위해 활용되는 가청 저주파수 영역대에서의 밴드갭이 극대화된 격자 구조를 제시한다.Abstract 1. Introduction 2. Isogeometric analysis of geometrically exact nonlinear structures 3. Isogeometric confinguration DSA of geometrically exact nonlinear structures 4. Numerical examples 5. Conclusions and future works A. Supplements to the geometrically exact Kirchhoff beam model B. Supplements to the geometrically exact shear-deformable beam model C. Supplements to the geometrically exact shear-deformable shell model D. Supplements to the invariant formulations E. Supplements to the geometric constraints in design optimization F. Supplements to the design of auxetic structures 초록Docto

Proceedings of the ECCOMAS Thematic Conference on Multibody Dynamics 2015

This volume contains the full papers accepted for presentation at the ECCOMAS Thematic Conference on Multibody Dynamics 2015 held in the Barcelona School of Industrial Engineering, Universitat Politècnica de Catalunya, on June 29 - July 2, 2015. The ECCOMAS Thematic Conference on Multibody Dynamics is an international meeting held once every two years in a European country. Continuing the very successful series of past conferences that have been organized in Lisbon (2003), Madrid (2005), Milan (2007), Warsaw (2009), Brussels (2011) and Zagreb (2013); this edition will once again serve as a meeting point for the international researchers, scientists and experts from academia, research laboratories and industry working in the area of multibody dynamics. Applications are related to many fields of contemporary engineering, such as vehicle and railway systems, aeronautical and space vehicles, robotic manipulators, mechatronic and autonomous systems, smart structures, biomechanical systems and nanotechnologies. The topics of the conference include, but are not restricted to: ● Formulations and Numerical Methods ● Efficient Methods and Real-Time Applications ● Flexible Multibody Dynamics ● Contact Dynamics and Constraints ● Multiphysics and Coupled Problems ● Control and Optimization ● Software Development and Computer Technology ● Aerospace and Maritime Applications ● Biomechanics ● Railroad Vehicle Dynamics ● Road Vehicle Dynamics ● Robotics ● Benchmark ProblemsPostprint (published version