ADINA Publications

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The Theory used in ADINA is richly documented in the following books by K.J. Bathe and co-authors


Finite Element Procedures
 

Finite Element Procedures in Engineering Analysis

Numerical Methods in Finite Element Analysis
 


The Mechanics of Solids and Structures — Hierarchical ...


The Finite Element Analysis of Shells — Fundamentals


Inelastic Analysis of Solids and Structures

 
 
To Enrich Life
(Sample pages here)
 

 

Following are more than 700 publications — that we know of — with reference to the use of ADINA. The pages give the Abstracts of some papers published since 1986 referring to ADINA. The most recent papers are listed first. All these papers may be searched using the box:

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Large-deformation analysis of nonlinear elastic fluids

Prost-Domasky, S.A. (Department of Mechanical Engineering, Washington University); Szabo, B.A.; Zahalak, G.I. Source: Computers and Structures, v 64, n 5-6, September, 1997, p 1281-1290

ISSN: 0045-7949 CODEN: CMSTCJ

Publisher: Elsevier Ltd

Abstract: A computational analysis was undertaken of four nonlinear generalizations of the simple Maxwell viscoelastic fluid under conditions of large deformations. The four fluids are named the upper convected Maxwell, lower convected Maxwell, Jaumann and Dong-Skalak-Sung fluids. Each of them is characterized by two material parameters, a shear modulus and a time constant and each reduces to the simple Maxwell fluid in the case of small, slow deformations. The finite element program ADINA was adapted to compute the mechanical responses of these materials to imposed surface displacements of various types. Our algorithm was based on the equality (for an incompressible material) of the components of the second Piola-Kirchhoff stress with respect to material coordinates and those of the Cauchy stress with respect to convected coordinates. After evaluating the algorithm's accuracy with respect to a limited set of available analytic solutions, the responses to indentation by a rigid, sharp-edged cylinder of a half-space composed of each of the four nonlinear fluids were computed. These calculations included a wide range of indentation speeds, covering the spectrum of material behavior from viscous fluid to hyperelastic solid. The computations admitted large indentations - up to six indenter radii in special cases. In contrast to their radically different behaviors when subjected to large homogeneous deformations, all four materials exhibited similar behaviors when subjected to deep indentations. For any specific choice of material and computational parameters, the computation terminated if the indentation became too deep and the magnitude of this maximum achievable indentation depth decreased with increasing mesh refinement. 1997 Elsevier Science Ltd. (12 refs.)

 

Numerical simulation of a BWR vessel lower head with penetration subjected to a postulated core damage accident

D. Azodi and P. Gruner

Gesellschaft für Anlagen und Reaktorsicherheit (GRS) mBH, Germany

Transactions of the 14th International Conf. on Structural Mechanics in Reactor Technology (SMiRT), 1997

Abstract: To assess the safety and the integrity of nuclear power plants in operation, hypothetical accidental events are considered, which – on account of their low frequency of occurrence – do not belong to design accidents. In this context, a global finite element (FE) model of a German BWR RPV lower head and a control rod nozzle was developed. The melt down time estimations were obtained by FE calculations of the temperature distributions, which consider the influence of the complex heat transfer into the RPV lower head and control rod nozzle as well as phase changing of steel material.

CORVIS. Investigation of light water reactor lower head failure modes

S. Brosi1, G. Duijvestijn1, H. Hirschmann1, B.S. Jäckel1, K. Nakada2, J.A. Patorski1, R. Rösel1, H.P. Seifert1, Ph. Tipping1

1 Laboratory jor Safety and Accident Research, Paul Scherrer lnstitut, CH-5232, Villigen PSL Switzerland
2Nuclear Engineering Laboratory, Toshiba Corporation, 4-1 Ukishima-cho, Kawasaki-ku, Kawasaki 210, Japan

Nuclear Engineering and Design, 168:77-104, 1997.

Abstract: The project CORVIS (Corium Reactor Vessel Interaction Studies) is a research programme for the experimental and analytical investigation of a possible failure of the pressure vessel of a light water reactor during an assumed core melt accident. The applied methods of the experimental technique, the metallurgical investigations and the computational analysis are described. Two recent melting experiments are presented in detail. The first experiment was carried out on a steel plate 100 mm thick representing a pressure vessel lower head without penetrations. The second experiment was performed on a steel plate of the same thickness but representing a boiling water reactor lower head carrying a tube penetration in the form of a drain line. Reported are the phenomenology of these experiments, the results of the metallurgical post-test examinations and the computational reconstruction of the observed heat transfer and ablation phenomena in a stagnant and in a turbulent melt. Further, the results of three earlier tests, on a smaller scale, are presented.

 

Analysis of vortex-induced vibration of cylindrical tubes in a cross flow

A.R. Massih, K. Forsberg and L. Plobeck

ABB Atom, Sweden

Proc. 14th Int. Conf. Reactor Technology (SMiRT 14), 1997

Abstract: In this paper we analyze the dynamic response of a circular cylinder in a cross flow using the wake oscillator model of Iwan and Blevins. We solve the nonlinear differential equation for the considered system utilizing both full numerical solution and an efficient algebraic analytical solution. In the latter we have approximated the displacement of the tube by truncated trigonometric series for which the resulting algebraic equations for the coefficients in the series provide a straightforward numerical solution for the amplitude of the oscillation versus the flow velocity. Our results are discussed in light of available experimental data. Lastly the computational fluid dynamics computer code ADINA-F is used to study the fluid structure interaction behavior of the system under consideration.

 

Advanced fuel elements for passive pressure tube light water reactors

P. Hejzlar, B.T. Mattingly, N.E. Todreas, M.J. Driscoll

Department of Nuclear Engineering, Massachusetts Institute of Technology, 77 Massachusetts Ave., Cambridge, MA 02139, USA

 

Nuclear Engineering and Design, 167:375-392, 1997

Abstract: This paper focuses on the development of advanced fuel elements for innovative pressure tube light water reactors. Considerations and constraints that affect the design process and various possible options are discussed. The two most promising fuel designs, which can survive a loss-of-coolant accident without primary coolant replenishment, while having sufficient margins to fuel design limits, are proposed, described and evaluated. It is demonstrated that this key objective can be achieved, provided that reliable SiC cladding or coating, which can withstand operating and accident conditions without failure, can be manufactured. Recent advances in ceramic coating technologies and experimental tests of coated specimens indicate that the attainment of this goal is feasible.

Keywords: Ceramic coatings — Light water reactors — Loss of coolant accidents — Nuclear fuel cladding — Pressure tube reactors — Silicon carbide

 

 

Modeling the annular incision in a herniated lumbar intervertebral disk to study its effect on disk stability

Natarajan, R.N. (Department of Orthopedic Surgery, Rush-Presbyt. St Luke's Med. Center); Andersson, G.B.J. Source: Computers and Structures, v 64, n 5-6, September, 1997, p 1291-1297

ISSN: 0045-7949 CODEN: CMSTCJ

Publisher: Elsevier Ltd

Abstract: Several techniques of lumbar disk annulotomy have been described in clinical reports, but have not addressed the influence of annulotomy type on motion-segment stability. The technique used to incise during diskectomy may play a role in the subsequent healing and biomechanical stability of the disk. The purpose of this study is to develop a finite-element model using ADINA to study the influence of annulotomy-technique selection on disk competence. The analyses showed that both the box- and slit-type annular incisions produced similar changes in the biomechanical characteristics of the disk excepting the stresses in the disk annulus. The study also showed that there is no preference between the two annular incisions as far as post-surgical stability of the disk is concerned. © 1997 Elsevier Science Ltd. (14 refs.)


FEM analysis and experimental research on complex forming

Xu, Shuqin (Taiyuan Univ of Technology); Fu, Yuan Source: Journal of Materials Processing Technology, v 69, n 1-3, Sep, 1997, p 208-211

ISSN: 0924-0136 CODEN: JMPTEF

Publisher: Elsevier Science S.A.

Abstract: Both upsetting and complex forming are simulated using plasticine as a model material, the evolution process of the holes in the cylinders being observed, the principle and the expected results of reducing the forming load of the process being analyzed by the theory of plasticity, and the strain distribution of the new process being predicted using FEM. The experimental results are found to coincide with the results of the analysis. Complex forming has bright prospects for industrial application. (5 refs.)

Keywords:  Metal forming  -  Finite element method  -  Plasticity  -  Strain  -  Computer software  -  Computer simulation

Secondary Keywords:  Plasticine  -  Software package ADINA

 


Modeling the thermal stresses at early ages in a concrete monolith

Ayotte, Eric; Massicotte, Bruno; Houde, Jules; Gocevski, Vladimir Source: ACI Materials Journal, v 94, n 6, Nov-Dec, 1997, p 577-587

ISSN: 0889-325X CODEN: AMAJEF

Publisher: American Concrete Inst

Abstract: This paper presents details of an experimental and numerical study of thermal strains and induced stresses in large-scale mass concrete. Three large-scale monoliths were built on a dam construction site in the James Bay Territory to monitor the thermal behavior of mass concrete subjected first to heat of hydration development and subsequent freeze and thaw cycles. The monoliths were instrumented with thermocouples and mechanical strain gages. The modeling of one monolith was carried out with computer program ADINA. The modeling includes the development of a heat of hydration curve typical to the concrete used in dam construction. The mechanical properties of early-age concrete were based on measurements or evaluated from various references. It is shown that, due to an inadequate representation of the reference temperature, many nonlinear incremental commercial software cannot correctly simulate the stress history of maturing concrete with the temperature variation. The paper presents a modified step-by-step approach which improved the stress modeling within the available commercial software. Excellent agreement between measured and computed temperatures and stresses was obtained. (10 refs.)

Keywords:  Concretes  -  Thermal stress  -  Concrete dams  -  Finite element method  -  Monitoring  -  Computer software  -  Strain gages

Secondary  Keywords:  Concrete monolith  -  Mass concrete  -  Freeze and thaw cycles

 


Dynamic elasto-plastic response of a generic vehicle floor model to coupled transient loads

Gupta, Aaron D. (U.S. Army Research Lab) Source: American Society of Mechanical Engineers, Pressure Vessels and Piping Division (Publication) PVP, v 351, Structures Under Extreme Loading Conditions, 1997, p 81-86

ISSN: 0277-027X CODEN: AMPPD5

Conference: Proceedings of the 1997 ASME Pressure Vessels and Piping Conference, Jul 27-31 1997, Orlando, FL, USA Sponsor: ASME

Publisher: ASME

Abstract: A dynamic elasto-plastic large displacement response analysis of the bottom floor of a generic vehicle hull model subjected to empirically obtained coupled blast and impact loads has been conducted using 3-D shell elements in the ADINA nonlinear dynamic finite-element analysis code. Although several simplifying assumptions are made regarding the structural model, material properties, and forcing functions, the investigation gives valuable insight into the nonlinear dynamic response behavior of a generic hull bottom floor to externally applied coupled blast and impact loads and provides an inexpensive method of evaluation of the structural integrity of modern vehicles subjected to spatially varying transient loads.

Keywords:  Vehicle parts and equipment  -  Dynamic response  -  Blast resistance  -  Elastoplasticity  -  Finite element method  -  Impact resistance  -  Structural analysis  -  Structural loads  -  Computer software  -  Computer simulation  -  Computer aided analysis

Secondary  Keywords:  Software package ADINA

 


Disposal of key problems in the FEM analysis of tube stagger spinning

Kemin, Xue (Harbin Inst of Technology); Yan, Lu; Xianming, Zhao Source: Journal of Materials Processing Technology, v 69, n 1-3, Sep, 1997, p 176-179

ISSN: 0924-0136 CODEN: JMPTEF

Publisher: Elsevier Science S.A.

Abstract: In connection with the problems which emerged when the ADINA FEM program was used to analyze the process of cylindrical workpiece stagger spinning theoretically, such as calculated model dispersion, the treatment of boundary conditions and the definition of load pattern, a set of useful solutions has been advanced. Experimentation has established that these methods are realistic, feasible and practicable. (3 refs.)

Keywords:  Metal forming  -  Finite element method  -  Computer software  -  Boundary conditions  -  Computer simulation

Secondary  Keywords:  Tube stagger spinning  -  Software package ADINA

 


Interface program development between CADDS5 and ADINA

Zhu, Yuqiao (China Inst of Atomic Energy); Li, Xiaofeng; Liu, Tiefu Source: Yuanzineng Kexue Jishu/Atomic Energy Science and Technology, v 31, n 2, Mar, 1997, p 98-105 Language: Chinese

ISSN: 1000-6931 CODEN: YKJIEZ

Publisher: Atomic Energy Publishing House

Abstract: A thorough CADDS5-ADINA analysis system was established by developing the interface program between CADDS5 and ADINA. The developed pre-processing interface program can transfer CADDS5 FEA models into ADINA models, and the developed postprocessing interface program converts the ADINA results into the format in compliance with the analyzer of CADDS5, then post-processor capabilities can be performed. By fully utilizing both the graphic processing capabilities of CADDS5 and the analysis capabilities of ADINA, the correctness is ensured, the computation time is saved, the intensity of data processing is reduced, and the capability to solve mechanical problems of sophisticated structures is improved. (5 refs.)

Keywords:  Computer software  -  Computer programming  -  Finite element method  -  Computer aided design

Secondary  Keywords:  Interface program  -  ADINA software  -  CADDS5 software


System and in-vessel severe accident phenomenology for a large PWR

Birchley, Jon (Paul Scherrer Inst); Duijvestijn, Guus Source: International Conference on Nuclear Engineering, Proceedings, ICONE, 1997, p 206

CODEN: 002541

Conference: Proceedings of the 1997 5th International Conference on Nuclear Engineering, ICONE5, May 25-29 1997, Nice, Fr Sponsor: ASME; SFEN; JSME

Publisher: ASME

Abstract: A series of studies using SCDAP/RELAP5 is performed for three postulated sequences in a 3-loop PWR of Siemens design. The thermal and mechanical response of lower head is performed using the ADINA finite element code package. The study addresses the likely range of internal pressure during the attack on the lower head by the core debris, how the pressure impacts on the failure process, and seeks to identify opportunities to mitigate the core melt and vessel failure sequences.

Keywords:  Core meltdown  -  Loss of coolant accidents  -  Pressurized water reactors  -  Pressure vessels  -  Computer software  -  Finite element method  -  Failure analysis

Secondary  Keywords:  Software Package ADINA  -  Heat rejection

 


Investigation on characteristic of J integral parameter in welded joints

Huo, Lixing (Tianjin Univ); Zhang, Yufeng; Kang, Jidong Source: China Welding (English Edition), v 6, n 1, May, 1997, p 11-18

ISSN: 1004-5341 CODEN: CWELEV

Publisher: China Welding

Abstract: The J integral parameter and its application feasibility in welded joints with different weldmatchings in yield strength (overmatching weld and undermatching weld), different material constitutive laws (material with a Ludes yield plateau and power hardening) and under different fracture types (ligament yielding fracture and general yielding fracture) are investigated. First the condition of J integral path independent has been studied based upon finite element analysis by using ADINA procedure on welded joints. It was shown that the J integral is path dependent for the cases studied in this paper. Then experiments were carried out to study availability of J integral as a plastic singularity parameter at the tip of the notch in welded joints. The results show that J dominance in most cases studied is not validated in v and u displacement fields. From both considerations mentioned above it can be concluded that J-integral as controlling parameter used to estimate the safety of welded structures is not always made clear. (3 refs.)

Keywords:  Welds  -  Yield stress  -  Fracture  -  Finite element method  -  Fracture mechanics  -  Mechanical properties  -  Strain  -  Cracks

Secondary  Keywords:  Integral parameter  -  Welded joints  -  Displacement fields  -  Plastic singularity

 


Constitutive model with capability to simulate complex multiaxial ratcheting behaviour of materials

Xia, Zihui (Univ of Alberta); Ellyin, Fernand Source: International Journal of Plasticity, v 13, n 1-2, 1997, p 127-142

ISSN: 0749-6419 CODEN: IJPLER

Publisher: Elsevier Science Ltd

Abstract: An elasto-plastic constitutive model developed by the authors has been further extended and implemented into a user-supplied material model in conjunction with a commercial Finite Element Model (FEM) code, ADINA. As benchmark problems, comprehensive experimental data by Jiang and Sehitoglu (1994a,b) are compared with the numerical predictions of the model as implemented in the ADINA code. It is clearly shown that this material model has a capability to simulate the complex multiaxial and multi-step ratcheting behaviour of metals and alloys. (17 refs.)

Keywords:  Elastoplasticity  -  Mathematical models  -  Finite element method  -  Computer software  -  Computer simulation

Secondary  Keywords:  Multiaxial ratcheting  -  Cyclic loading  -  Software package ADINA

 


Folsom spillway gate failure and lessons learned

Todd, Robert V. (United States Bur of Reclamation) Source: Proceedings, Congress of the International Association of Hydraulic Research, IAHR, v D, Energy and Water: Sustainable Development, 1997, p 66-71

CODEN: PCIRD3

Conference: Proceedings of the 1997 27th Congress of the International Association of Hydraulic Research, IAHR. Part D, Aug 10-15 1997, San Francisco, CA, USA Sponsor: ASCE

Publisher: ASCE

Abstract: Spillway Tainter gate No.3 failed at Folsom Dam, CA, on July 17, 1995, resulting in a discharge of 1,132 m3/s into the lower American River. The gate is one of five service spillway gates 12.8 m wide by 15.2 m high. There are also three other emergency spillway gates, with the same width, but 15.9 m high. An action team was first established comprising personnel from the US Army Corps of Engineers and the Bureau of Reclamation to design reinforcements for the remaining seven gates, and to design a new gate to replace the failed one. Because of the importance of determining the actual failure mode, a forensic team is formed which turned into a multi-disciplinary, multi-agency team which were found to be a very good decision. (1 refs.)

Keywords:  Spillway gates  -  Dams  -  Failure analysis  -  Structural analysis  -  Friction  -  Finite element method  -  Modal analysis  -  Inspection  -  Computer software  -  Computer aided analysis

Secondary  Keywords:  Software package ADINA

 


Benchmark calculations for mechanical stresses upon a transport cask

Dreier, G. (Gesellschaft fuer Nuklear-Behaelter mbH); Diersch, R.; Hueggenberg, R.; Spilker, H.; Bantle, S. Source: Nuclear Engineering and Design, v 176, n 3, Dec 4, 1997, p 207-214

ISSN: 0029-5493 CODEN: NEDEAU

Publisher: Elsevier Science S.A.

Abstract: In this paper, benchmark calculations are carried out using the FEM code ADINA. Three drop tests with a DCI cask carried out in Japan are investigated. The drop orientations comprise the 9 m drop with impact flat onto the cylindrical shell of the shock absorbers at the top and bottom part as well as the 1 m drop with impact of the bar in the center of the cylinder wall. Calculated results are compared to the experimental ones. It is found that the calculations meet the measurements conservatively. (9 refs.)

Keywords:  Nuclear engineering  -  Stresses  -  Finite element method  -  Computer software  -  Computational methods

Secondary  Keywords:  Software package ADINA  -  Transport cask

Non-linear seismic cracking analysis of medium-height concrete gravity dams

M. Mao and C. A. Taylor

Earthquake Engineering Research Centre, Department of Civil Engineering, University of Bristol, Queens Building, University Walk, Bristol, BS8 ITR, U.K.

Computers & Structures , 64:1197-1204, 1997

Abstract: The non-linear dynamic response of concrete gravity dams under seismic loads is a little-understood phenomenon due to limitations in the previous studies. The choice of a reliable concrete constitutive model and constitutive parameters to predict the performance of concrete gravity dams under severe earthquake ground motion is one of the most complex tasks. The response of a typical medium-height concrete gravity dam to a realistic motion is examined using the ADINA concrete model. The fracture energy cracking criterion is applied to remove the unreasonable mesh sensitivity of the results. The influence of the constitutive oarameters on the earthquake response analysis of concrete gravity dams is also discussed.

 


Optimization of the manufacturing process of a titanium aluminide metal matrix composite using a viscoplastic constitutive theory

Sherwood, James A. (Univ of Massachusetts at Lowell); Quimby, Howard M. Source: American Society of Mechanical Engineers, Materials Division (Publication) MD, v 74, Advanced Materials: Development, Characterization Processing, and Mechanical Behavior, 1996, p 53-54

CODEN: AMEMD9

Conference: Proceedings of the 1996 ASME International Mechanical Engineering Congress and Exposition, Nov 17-22 1996, Atlanta, GA, USA Sponsor: ASME

Publisher: ASME

Abstract: The time-dependent thermomechanical behavior of a silicon-carbide-fiber reinforced titanium-aluminide matrix composite systems and the residual stress state developed upon cooldown which initiates matrix cracking, was investigated using a three-dimensional model. However, based on the information gained from the three-dimensional model, it was concluded that an axisymmetric two-dimensional model would be sufficient and computationally more efficient. Contact surfaces were used to model the fiber matrix interface. The use of the contact option to model the fiber/matrix interface assumes that the bonding of the fiber to the matrix was a consequence of mechanical bonding only called weak bonding. (3 refs.)

Keywords:  Metallic matrix composites  -  Fiber reinforced metals  -  Viscoplasticity  -  Interfaces (materials)  -  Finite element method  -  Mathematical models  -  Computer software  -  Silicon carbide  -  Titanium  -  Aluminum compounds

Secondary  Keywords:  Software package ADINA

 


Temperature distribution in a cylindrical Al2O3-steel joint during the vacuum brazing cycle

Golanski, D. (Warsaw Univ of Technology) Source: Journal of Materials Processing Technology, v 56, n 1-4, Jan, 1996, p 945-954

ISSN: 0924-0136 CODEN: JMPTEF

Conference: Proceedings of the 1993 International Conference on Advances in Material & Processing Technologies, AMPT'93, Aug 1993, Dublin, Irel

Publisher: Elsevier Science Inc

Abstract: This paper deals with the investigations of temperature distribution during vacuum brazing of cylindric Al2O3 and steel samples, using the AgCuInTi active filler metal. The thermovision system AGA 680S was used to register the temperature field during brazing cycle. Bonded joints were observed by the infrared scanner unit during heating, brazing and cooling. Two types of joints with different shape of steel element were examined during temperature measurements. Additionally, a 2D finite element code 'ADINA-T' was used to solve for the problem of nonlinear transient thermal analysis of temperature distribution in the axisymmetric models of Al2O3-steel brazed joints. The experimental results revealed the presence of big transient axial temperature drops in the ceramic part. The change of metal shape resulted in a reduction of the transient temperature drops in the ceramic element. The finite element calculations corresponded well with the results of measurements and showed that the perfect thermal contact between adjacent surfaces plays the important role in heat transfer and can be a factor affecting temperature gradients in ceramic. (4 refs.)

Keywords:  Joints (structural components)  -  Steel  -  Vacuum brazing  -  Temperature distribution  -  Alumina  -  Filler metals  -  Heating  -  Cooling  -  Temperature measurement  -  Finite element method  -  Thermoanalysis  -  Calculations  -  Mathematical models

Secondary  Keywords:  Cylindrical alumina steel joint  -  Vacuum brazing cycle  -  Bonded joints  -  Axial temperature drops  -  Finite element code  -  Thermal contact  -  Nonlinear transient thermal analysis  -  Thermovision system

 


Response of lime mortar joint arches to moving loads

Rosson, Barry T. (Univ of Nebraska); Boothby, Thomas E.; Soyland, Ketil Source: Structures Congress - Proceedings, Worldwide Advances in Structural Concrete and Masonry, 1996, p 223-232

CODEN: 85SCAP

Conference: Proceedings of the 1996 CCMS of the ASCE Symposium in Conjunction with Structures Congress XIV, Apr 15-18 1996, Chicago, IL, USA Sponsor: ASTM

Publisher: ASCE

Abstract: The response of masonry arch bridges to moving wheel loads was simulated in the laboratory by constructing four half-scale arches with a span length of 1.22 m, using 17 voussoirs and lime mortar joints. The moving loads varied from 115 kg to 910 kg and were simulated by hanging steel weights from the center-of-gravity of the voussoirs. The finite element program ADINA was used to model the arch ring using 13,312 8-node isoparametric elements. Experimental results show the lime mortar joints exhibit significant plastic deformation accumulations with the first few cycles of loading, then diminish during subsequent load cycles. When the Drucker-Prager material model is used for the lime mortar, the FEM results indicate the plastic accumulations do not occur after the first load cycle. It is believed that sliding occurs between the voussoirs and the mortar, producing small cyclical deformations under moving loads. The four arches were also monotonically loaded to collapse in the laboratory, and the FEM stress variations normal to the mortar joints are illustrated for this loading condition. (7 refs.)

Keywords:  Masonry bridges  -  Dynamic response  -  Arches  -  Loads (forces)  -  Joints (structural components)  -  Lime  -  Finite element method  -  Mathematical models  -  Mortar  -  Plastic deformation  -  Stress analysis  -  Computer simulation

Secondary  Keywords:  Moving loads  -  Voussoirs  -  Center of gravity  -  Stress variations  -  Lime mortar joint arches

 



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